Local Connectedness Research Articles

Local connectedness of boundaries for relatively hyperbolic groups

AbstractLet be a relatively hyperbolic group pair that is relatively one ended. Then, the Bowditch boundary of is locally connected. Bowditch previously established this conclusion under the additional assumption that all peripheral subgroups are finitely presented, either one or two ended, and contain no infinite torsion subgroups. We remove these restrictions; we make no restriction on the cardinality of and no restriction on the peripheral subgroups .

Global shocks and local connectedness: evidence from dynamic tail risk interdependences among Chinese regional carbon markets

ABSTRACT This paper analyzes tail risk interdependence among four regional carbon markets in China to investigate the effect of exogenous shocks on local connectedness. We utilize a time-varying copulas approach and find that: (i) the Shenzhen carbon market has the highest level of tail risk due to the lower liquidity and weaker resilience. (ii) Carbon markets where prices are more responsive to information have higher levels of tail risk dependence. (iii) Compared to the China – US trade dispute and the armed conflict in Europe, the shocks from the extreme weather and the COVID-19 outbreak can prominently strengthen tail risk.

Uniform Local Connectedness and Completion of Metric σ-Frames

ABSTRACT We extend the notion of local connectedness and uniform local connectedness to the category M σ Frm of metric σ-frames. We provide the construction of the uniformly locally connected reflection of a locally connected metric σ-frame. We also discuss complete metric σ-frames and show the existence of a completion for a metric σ-frame in the category M σ Frm.

Increasing sequence of T0-topologies on the set of positive integers

In this paper we introduce, similarly as it was done in [11] for Kirch's type topologies, a sequence of topologies Tm that are subtopologies of the common division topology T. The sum of all topologies Tm is the common division topology. We also show that all topologies Tm are T0 and they are not T1 on N, examine properties of prime numbers and characterize connectedness of arithmetic progressions in each of the topology Tm. An immediate consequence of these characterizations is local connectedness of the space (N,Tm) for each m∈N.

The place of rural hospitals in New Zealand's health system: an exploratory qualitative study.

In Aotearoa New Zealand (NZ) there is a knowledge gap regarding the place and contribution of rural hospitals in the health system. New Zealanders residing in rural areas have poorer health outcomes than those living in urban areas, and this is accentuated for Māori, the Indigenous people of the country. There is no current description of rural hospital services, no national policies and little published research regarding their role or value. Around 15% of New Zealanders rely on rural hospitals for health care. The purpose of this exploratory study was to understand national rural hospital leadership perspectives on the place of rural hospitals in the NZ health system. A qualitative exploratory study was undertaken. The leadership of each rural hospital and national rural stakeholder organisations were invited to participate in virtual semi-structured interviews. The interviews explored participants' views of the rural hospital context, the strengths and challenges they faced and how good rural hospital care might look. Thematic analysis was undertaken using a framework-guided rapid analysis method. Twenty-seven semi-structured interviews were conducted by videoconference. Two broad themes were identified, as follows. Theme 1, 'Our place and our people', reflected the local, on-the-ground situation. Across a broad variety of rural hospitals, geographical distance from specialist health services and community connectedness were the common key influencers of a rural hospital's response. Local services were provided by small, adaptable teams across broad scopes and blurred primary-secondary care boundaries, with acute and inpatient care a key component. Rural hospitals acted as a conduit between community-based care and city-based secondary or tertiary hospital care. Theme 2, 'Our positioning in the wider health system', related to the external wider environment that rural hospitals worked within. Rural hospitals operating at the margins of the health system faced multiple challenges in trying to align with the urban-centric regulatory systems and processes they were dependent on. They described their position as being 'at the end of the dripline'. In contrast to their local connectedness, in the wider health system participants felt rural hospitals were undervalued and invisible. While the study found strengths and challenges common to all NZ rural hospitals, there were also variations between them. This study furthers understanding of the place of rural hospitals in the NZ healthcare system as seen through a national rural hospital lens. Rural hospitals are well placed to provide an integrative role in locality service provision, with many already long established in performing this role. However, context-specific national policy for rural hospitals is urgently needed to ensure their sustainability. Further research should be undertaken to understand the role of NZ rural hospitals in addressing healthcare inequities for those living in rural areas, particularly for Māori.

Connectedness, local connectedness, and components on bipolar soft generalized topological spaces

Connectedness represents the most significant and fundamental topological property. It highlights the main characteristics of topological spaces and distinguishes one topology from another. There is a constant study of bipolar soft generalized topological spaces (\( \mathcal{BSGTS}s \)) by presenting \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected set and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected space in \(\mathcal{BSGTS}s\) as well as it is discussing some properties and results for these topics. Additionally, the notion of bipolar soft disjoint sets is put forward, \(\mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-separation set, \(\widetilde{\widetilde{\mathfrak{g}}}\)-separated \(\mathcal{BSS}s\) and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-hereditary property. Moreover, there is an extensive study of \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-locally connected space and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-component with some related properties and theorems following them, such as the concepts of \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-locally connected spaces and \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected are independent of each other; also determined the conditions under which the \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected subsets are \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-components.

A resilient and connected network of sites to sustain biodiversity under a changing climate

Motivated by declines in biodiversity exacerbated by climate change, we identified a network of conservation sites designed to provide resilient habitat for species, while supporting dynamic shifts in ranges and changes in ecosystem composition. Our 12-y study involved 289 scientists in 14 study regions across the conterminous United States (CONUS), and our intent was to support local-, regional-, and national-scale conservation decisions. To ensure that the network represented all species and ecosystems, we stratified CONUS into 68 ecoregions, and, within each, we comprehensively mapped the geophysical settings associated with current ecosystem and species distributions. To identify sites most resilient to climate change, we identified the portion of each geophysical setting with the most topoclimate variability (high landscape diversity) likely to be accessible to dispersers (high local connectedness). These "resilient sites" were overlaid with conservation priority maps from 104 independent assessments to indicate current value in supporting recognized biodiversity. To identify key connectivity areas for sustaining species movement in response to climate change, we codeveloped a fine-scale representation of human modification and ran a circuit-theory-based analysis that emphasized movement potential along geographic climate gradients. Integrating areas with high values for two or more factors, we identified a representative, resilient, and connected network of biodiverse lands covering 35% of CONUS. Because the network connects climatic gradients across 250,000 biodiversity elements and multiple resilient examples of all geophysical settings in every ecoregion, it could form the spatial foundation for targeted land protection and other conservation strategies to sustain a diverse, dynamic, and adaptive world.

A Study on Some Language Impairments in Patients with Lewy Body Spectrum Disorders

Objectives: This study aimed to evaluate some speech disorders in groups of patients with Lewy body spectrum disorders (LBSD), compare the groups in order to identify the possible causes of the disorders, and improve the given patients’ quality of life by helping them manage the development of speech disorders and rehabilitation of them. Methods: The present case-control study was performed to examine a total of 40 individuals, including 10 healthy people as controls and 30 patients with a range of LBSD diagnosed based on the criteria for cognitive neurological and motor disorders published by the University of Pennsylvania Department of Neurology. Results: The four groups were similar in age and sex distribution and were not statistically and significantly different. The highest score of short mental state test (MMSE) was obtained for the control group. Parkinson’s patients with dementia spent the longest time to tell the story. The highest number of sentences was also produced by the Parkinson’s disease (PD) group. The control group faced the least number of vocabulary retrieval problems when narrating the story. On the other hand, the most frequent word retrieval problem was observed in dementia with Lewy bodies, followed by Parkinson’s disease with dementia (PDD). There was a significant difference between the control group with dementia and the Lewy body in terms of frequency distribution of action and search theme. There were also significant differences among four groups regarding the global and local connectedness of storytelling as well as the number of keywords used. Conclusions: In sum, a considerable speech disorder was observed in patients with LBSD, which was more evident in two groups with dementia. Therefore, dementia may have been the main cause of these impairments.

Every component of a fractal square is a Peano continuum

This paper concerns the local connectedness of components of self-similar sets. Let n≥2 be an integer and let D⊂{0,1,…,n−1}2. The self-similar set F satisfying F=⋃d∈D(F+d)/n is called a fractal square. We prove that every component of F is locally connected. The same result for three-dimensional analogues of F does not hold.

Epidemic risk assessment from geographic population density

The geographic distribution of the population on a region is a significant ingredient in shaping the spatial and temporal evolution of an epidemic outbreak. Heterogeneity in the population density directly impacts the local relative risk: the chances that a specific area is reached by the contagion depend on its local density and connectedness to the rest of the region. We consider an SIR epidemic spreading in an urban territory subdivided into tiles (i.e., census blocks) of given population and demographic profile. We use the relative attack rate and the first infection time of a tile to quantify local severity and timing: how much and how fast the outbreak will impact any given area. Assuming that the contact rate of any two individuals depends on their household distance, we identify a suitably defined geographical centrality that measures the average connectedness of an area as an efficient indicator for local riskiness. We simulate the epidemic under different assumptions regarding the socio-demographic factors that influence interaction patterns, providing empirical evidence of the effectiveness and soundness of the proposed centrality measure.

Increasing sequence of topologies on the set of positive integers

In this paper we deal with topologies defined on the set of positive integers. We introduce a sequence of topologies Dm that are subtopologies of Golomb's topology D. The sum of all topologies Dm is Golomb's topology. We show also that all topologies Dm are Haudsdorff but not regular on N. Further, we characterize connectedness of arithmetic progressions in each topology Dm. An immediate consequence of these characterizations is local connectedness of the space (N,Dm) for each m∈N.

The Distance Matching Extension in K1,k-free Graphs with High Local Connectedness

The Distance Matching Extension in K1,k-free Graphs with High Local Connectedness

On the hyperspace $C_n(X)/{C_n}_K(X)$

Let $X$ be a continuum and $n$ a positive integer. Let $C_n(X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components, endowed with the Hausdorff metric. For $K$ compact subset of $X$, define the hyperspace ${C_n}_K(X)=\{A\in C_n(X)\colon K\subset A\}$. In this paper, we consider the hyperspace $C_K^n(X)=C_n(X)/{C_n}_K(X)$, which can be a tool to study the space $C_n(X)$. We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility.

Connectedness and Local Connectedness on Infra Soft Topological Spaces

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components.

Locally symmetrically connected T 0-quasi-metric spaces

Following the theory of symmetrically connected T 0-quasi-metric spaces constructed lately, in the present investigation the authors introduce and study the localized version of symmetric connectedness under the name local symmetric connectedness, as a new approach to determining the degree of the asymmetry and symmetry of T 0-quasi-metric spaces. In this context, some properties and topological aspects of locally symmetrically connected T 0-quasi-metric spaces are discussed by presenting various observations and many concrete (counter)examples. Specifically, it is shown that symmetric connectedness coincides with the local symmetric connectedness if we deal with the T 0-quasi-metric induced by an asymmetric norm which associates the theory of quasi-metrics in asymmetric topology with functional analysis.

On equicontinuous factors of flows on locally path-connected compact spaces

AbstractWe consider a locally path-connected compact metric space K with finite first Betti number $\textrm {b}_1(K)$ and a flow $(K, G)$ on K such that G is abelian and all G-invariant functions $f\,{\in}\, \textrm{C}(K)$ are constant. We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than ${\textrm {b}_1(K)}/{\textrm {b}_0(K)}$ . For this purpose, we use and provide a new proof for Theorem 2.12 of Hauser and Jäger [Monotonicity of maximal equicontinuous factors and an application to toral flows. Proc. Amer. Math. Soc.147 (2019), 4539–4554], which states that for a flow on a locally connected compact space the quotient map onto the maximal equicontinuous factor is monotone, i.e., has connected fibers. Our alternative proof is a simple consequence of a new characterization of the monotonicity of a quotient map $p\colon K\to L$ between locally connected compact spaces K and L that we obtain by characterizing the local connectedness of K in terms of the Banach lattice $\textrm {C}(K)$ .

Genre Features and Types of Adyghe Toponymic Legends

The article examines the Adyghe toponymic traditions. The relevance of the work is that it addresses one of the complex theoretical problems of modern Russian folklore — the definition of differentiating genre features of works of oral folk prose. The authors proceed from the fact that the identification of genre characteristics of Adyghe toponymic legends should contribute to the creation of a generalizing genre system of Adyghe folk non-fairy prose. The novelty of the research consists in determining the genre features of Adyghe toponymic legends and their classification. In the continuum of Adyghe toponymic traditions, two groups are distinguished: the traditions of the first group are archaic, they tell about the events of the distant past and are known throughout the entire ethnic territory. It is shown that the plot of this type of legend is expanded, complicated and includes a number of additional motives — the history of migration and settlement of the current territories by the people, genealogical excursions. It is noted that another group of toponymic legends is associated with events of the recent past and has a narrow local connectedness. The marker of historical authenticity of the described facts and events is an indication of real historical persons who act as characters in the legend. It is argued that the plot of this type of legend is not developed, they are usually one-episode, and the area of distribution of this group of legends is usually limited to one locality.

Connecting at Local Level: Exploring Opportunities for Future Design of Technology to Support Social Connections in Age-Friendly Communities.

Social connectedness in later life is an important dimension of an age-friendly community, with associated implications for individual health and wellbeing. In contrast with prior efforts focusing on connections at a distance or online communities where the digital technology is the interface, we explore the design opportunities and role of technology for connectedness within a geographically local community context. We present findings from interviews with 22 older adults and a linked ideation workshop. Our analysis identified shared concerns and negative perceptions around local relationships, connections and characteristics of the geographical area. However, local connectedness through technology was largely absent from day-to-day life and even perceived as contributing to disconnection. By uncovering how older adults use and perceive technology in their social lives and combining these findings with their ideas for improving local connections, we highlight the need for thoughtful consideration of the role of technology in optimising social connections within communities. Our research highlights a need for design work to understand the specifics of the local context and reduce emphasis on technology as the interface between people. We introduce an amended definition—‘underpinned by a commitment to respect and social inclusion, an age-friendly community is engaged in a strategic and ongoing process to facilitate active ageing by optimising the community’s physical, social and digital environments and its supporting infrastructure’—to conceptualise our approach. We conclude by suggesting areas for future work in developing digitally connected age-friendly communities.

Increasing strong size properties and strong size block properties

Let X be a continuum. The n-fold hyperspace Cn(X), n∈N, is the family of all nonempty closed subsets of X with at most n components, topologized with the Hausdorff metric. Let μ be a strong size map for Cn(X). A strong size level is the subset μ−1(t), with t∈[0,1]. A strong size block is the subset μ−1([s,t]), with 0≤s<r≤1. A topological property P is said to be a increasing strong size property provided that if μ is a strong size map for Cn(X) and t0∈[0,1), is such that μ−1(t0) has property P, then so does μ−1(t) for each t∈(t0,1). In this paper we show that uniform pathwise connectedness, uniform continuum-chainability and local connectedness are increasing strong size properties, and we will show some strong size block properties.

International connectedness and local disconnectedness: MNE strategy, city-regions and disruption.

Much of the rising international connectedness of city-regions has developed from MNEs replacing local connections with (superior) international ones. This often creates local disconnectedness that energizes the current populist backlash against MNE activities. We develop approaches to new IB theory, addressing the interdependencies of MNEs and city-regions that we propose as a crucial avenue for future research. We contrast two generic MNE strategies. The first is the traditional one: the ‘global orchestration’ of resources and markets. We argue that it exacerbates local disconnectedness. The second, that we call ‘local spawning,’ involves engaging with the local entrepreneurial eco-system to create and renew local connectedness, diffusing populist responses. Some MNEs are better able to implement a local spawning strategy, due to industry factors like innovation clock-speed, and firm characteristics like organizational path dependency. Finally, we distinguish between disconnection, which is an outcome of MNE strategy, and global disruptions, like the coronavirus (COVID-19) pandemic, which are primarily stochastic events. Addressing disconnections requires MNEs to re-orient their strategies while dealing with disruptions requires undertaking risk mitigation. We present empirical evidence from city-regions around the world to illustrate our theory.