Soft Spaces Research Articles

Introduction to Neutrosophic Soft Bitopological Spaces

In this study, the concept of neutrosophic soft bitopological space is defined and it is one of the few studies that have dealt with this concept. In addition, pairwise neutrosophic soft open (closed) set on neutrosophic soft bitopological spaces are studied. Supra neutrosophic soft topology is defined by pairwise neutrosophic soft open sets. Important theorems related to the subject supported with many examples for a better understanding of the subject are given.

Soft $ \alpha $-separation axioms and $ \alpha $-fixed soft points

<abstract> Soft set theory is a theme of interest for many authors working in various areas because of its rich potential for applications in many directions. it received the attention of the topologists who always seeking to generalize and apply the topological notions on different structures. To contribute to this research area, in this paper, we formulate new soft separation axioms, namely $ tt $-soft $ \alpha T_i\; (i = 0, 1, 2, 3, 4) $ and $ tt $-soft $ \alpha $-regular spaces. They are defined using total belong and total non-belong relations with respect to ordinary points. This way of definition helps us to generalize existing comparable properties via general topology and to remove a strict condition of the shape of soft open and closed subsets of soft $ \alpha $-regular spaces. With the help of examples, we show the relationships between them as well as with soft $ \alpha T_i\; (i = 0, 1, 2, 3, 4) $ and soft $ \alpha $-regular spaces. Also, we explore under what conditions they are kept between soft topological space and its parametric topological spaces. We characterize $ tt $-soft $ \alpha T_1 $ and $ tt $-soft $ \alpha $-regular spaces and give some conditions that guarantee the equivalence of $ tt $-soft $ \alpha T_i\; (i = 0, 1, 2) $ and the equivalence of $ tt $-soft $ \alpha T_i\; (i = 1, 2, 3) $. Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces and sum of soft topological spaces. In the end, we study the main properties of of $ \alpha $-fixed soft point theorem. </abstract>

Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is ( space if each coordinate space is soft space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of t t -soft semi- T i i = 0 , 1 , 2 , 3 , 4 and t t -soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi- T i i = 0 , 1 , 2 , 3 , 4 and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a t t -soft semiregular space and demonstrate that it guarantees the equivalence of t t -soft semi- T i i = 0 , 1 , 2 . Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.

An isomorphic approach of fuzzy soft lattices to fuzzy soft Priestley spaces

The main purpose of this paper is to establish a relation between fuzzy soft lattices and fuzzy soft Priestley spaces. We have proved that each bounded distributive lattice of fuzzy soft sets is isomorphic to the lattice of all clopen upsets of a Priestley space. For this reason, we have defined fuzzy soft upsets, fuzzy soft downsets, fuzzy soft filters, fuzzy soft ideals and fuzzy soft Priestley space. To endorse the above relation, we have proved some related results.

Effect of air supply mode on the airflow distribution inside soft sleeper compartments of air-conditioned trains

Trains are an important means of transportation for people to travel. The train's soft sleeper compartment space is relatively small, and the density of people is relatively large. Therefore, improving the thermal comfort and air quality of the compartment is of great significance for ensuring a healthy travel environment. To analyze the appropriate mode of conditioned air supply in train soft sleeper compartments, the airflow distribution inside soft sleeper compartments is simulated numerically at four different air supply modes, namely, sidewall air supply with slot diffusers, perforated ceiling air supply, bedside task–ambient air conditioning, and displacement ventilation. The reliability of the numerical simulation models is verified with the experimental data in the literature. Comparative analysis is made in terms of the compartment temperature, velocity, predicted mean vote and predicted percentage dissatisfied (PMV-PPD), and ventilation efficiency among various modes of air supply. The four air supply schemes are evaluated comprehensively by stochastic multicriteria acceptability analysis (SMAA-2). As the computational results show, bedside task–ambient air conditioning is the best air supply mode in terms of comprehensive performance indicators, followed by the sidewall slot air supply. The perforated ceiling air supply ranks third, and is superior to displacement ventilation.

Weak Forms of Soft Separation Axioms and Fixed Soft Points

Realizing the importance of separation axioms in classifications of topological spaces and studying certain properties of fixed points, we formulate new soft separation axioms, namely tt-soft and tt-soft b-regular spaces. Their definitions depend on three factors: soft b-open sets, total belong and total non-belong relations. In fact, they are genuine generalizations of p-soft -spaces in the cases of i = 0, 1, 2. With the help of examples, we study the relationships between them as well as with soft and soft b-regular spaces. Some interesting properties of them are obtained under the conditions of soft hyperconnected and extended soft topological spaces. Also, we show that they are preserved under finite product soft spaces and soft -homeomorphism mappings. Finally, we introduce a concept of b-fixed soft points and investigate its main properties.

Separation Axioms in Soft Tritopological Spaces with Respect to Ordinary Points

Separation Axioms in Soft Tritopological Spaces with Respect to Ordinary Points

Mappings and Connectedness on Hesitant Fuzzy Soft Multispaces

In this paper, we introduce the concept of mapping on hesitant fuzzy soft multisets and present some results for this type of mappings. The notions of inverse image and identity mapping are defined, and their basic properties are investigated. Hence, kinds of mappings and the composition of two hesitant fuzzy soft multimapping with the same dimension are presented. The concept of hesitant fuzzy soft multitopology is defined, and certain types of hesitant fuzzy soft multimapping such as continuity, open, closed, and homeomorphism are presented in detail. Also, their properties and results are studied. In addition, the concept of hesitant fuzzy soft multiconnected spaces is introduced.

Sum of Soft Topological Spaces

In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft T i , soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces.

On soft pc-separation axioms

AbstractMany mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological spaceX. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft{p}_{c}-{T}_{i}and soft{p}_{c}-{T}_{i}^{\ast },i=0,1,2by using the concept of soft{p}_{c}-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.

Together, not alongside! Strategies for the development of inter-municipal cooperation in the Stadtregion,of Vienna

The urban region of Vienna (Stadtregion+) is among the most dynamic growth regions in Europe. The management of the population growth poses extensive challenges for the city and its hinterland requiring a common and coordinated procedure. The urban regional cooperation structures are currently weakly institutionalised and barely defined. Against this background, this paper aims at presenting recommendations for the development of informal-cooperative spatial development processes in city regions on an analytical and instrumental level. The theoretical framework is based on a combination of the concept of strategic planning and the approach of soft spaces. The methods include the analysis of functional interconnections, a network analysis as well as the calculation of an interconnection index. By means of the “paradox of interconnection and cooperation” the totally different structures of the city-regional functional interconnections and the inter-municipal cooperation are shown on an analytical level. On an instrumental level, the planning principle of “flexible regionalisation” is presented, which draws upon and further develops the idea of spatial and temporal flexibility in strategic planning. A central element of this principle is the identification of “urban-regional focus areas” defined as specific areas within the urban region. These focus areas are characterised as soft planning spaces, in which to work on common planning and development challenges in an inter-municipal, cooperative and implementation-oriented manner. The applied methods and its findings are critically reflected and discussed, before deriving Vienna-specific and general policy recommendations.

Invertible Operators on Soft Normed Spaces

Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator. We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

Novel of soft sets and soft topologies in soft ideal spaces

As a result of the great development in all fields of life that created several problems which need to be solved, so it became necessary for the scientists to reconsider the numbers theory and develop it accordingly to solve these problems at a time a new science appeared that is of soft set theory which was regarded as important tool to solve a lot of problem in different domains in economics, engineering and medicine and others. In this paper, we present new of soft set which is -soft, -soft and -soft sets in soft ideal spaces and study their properties. We obtain characterization for soft compatible ideal via -soft sets, also, a generalized soft topology via soft ideal is finer than by using -soft sets.

Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem

This study introduces a new family of soft separation axioms and a real-life application utilizing partial belong and natural non-belong relations. First, we initiate the concepts of w-soft $$T_i$$ -spaces $$(i=0, 1, 2, 3, 4)$$ with respect to distinct ordinary points. These concepts generate a wider family of soft spaces compared with soft $$T_i$$ -spaces, p-soft $$T_i$$ -spaces and e-soft $$T_i$$ -spaces. We illustrate the relationships between w-soft $$T_i$$ -spaces with the help of examples and discuss some sufficient conditions of soft topological spaces to be w-soft $$T_i$$ -spaces. Additionally, we point out that stable or soft regular spaces are sufficient conditions for the equivalence among the concepts of soft $$T_i$$ , p-soft $$T_i$$ and w-soft $$T_i$$ . We highlight on explaining the links between w-soft $$T_i$$ -spaces and their parametric topological spaces and studying the role of enriched spaces in these links. Furthermore, we prove that w-soft $$T_i$$ -spaces are hereditary and topological properties, and they are preserved under finite product soft spaces. Finally, we propose an algorithm to bring out the optimal choices. This algorithm is based on dividing the whole parameters set into parameter sets and then apply a partial belong relation in the favorite soft sets. This application is supported with an interesting example to show how to implement this algorithm.

Brexit Geographies: Spatial Imaginaries and Relational Territorialities on the Island of Ireland

The pending exit of the United Kingdom from the European Union has far-reaching consequences for the political geography of the island of Ireland. The current territorial settlement founded on the 1998 Good Friday Agreement (GFA) was made possible by the common membership of Ireland and the UK of the European Union. The logic of the Good Friday Agreement replaced competing territorial claims with a settlement whereby the territoriality of Northern Ireland has shifted from that of a bounded container space within the UK to a relational space, dependent on North- South-and Ireland-UK relations within the broader European context. Brexit continues to represent a moment of critical transformation with as yet very uncertain outcomes. This paper explores the potential for a nuanced understanding of the ‘island of Ireland’ and Irish border region pre- and post-Brexit, as liminal ‘soft spaces’; spaces of possibility located outside the formal spheres of nation-state territoriality, but nevertheless very much located within the shadow of territory.

Two new forms of ordered soft separation axioms

AbstractThe goal of this work is to introduce and study two new types of ordered soft separation axioms, namely soft Ti-ordered and strong soft Ti-ordered spaces (i = 0, 1, 2, 3, 4). These two types are formulated with respect to the ordinary points and the distinction between them is attributed to the nature of the monotone neighborhoods. We provide several examples to elucidate the relationships among these concepts and to show the relationships associate them with their parametric topological ordered spaces and p-soft Ti-ordered spaces. Some open problems on the relationships between strong soft Ti-ordered and soft Ti-ordered spaces (i = 2, 3, 4) are posed. Also, we prove some significant results which associate both types of the introduced ordered axioms with some notions such as finite product soft spaces, soft topological and soft hereditary properties. Furthermore, we describe the shape of increasing (decreasing) soft closed and open subsets of soft regularly ordered spaces; and demonstrate that a condition of strong soft regularly ordered is sufficient for the equivalence between p-soft T1-ordered and strong soft T1-ordered spaces. Finally, we establish a number of findings that associate soft compactness with some ordered soft separation axioms initiated in this work.

Topologized Soft Fundamental Group of Soft Topological Group

In this paper, we show that each soft topological group is a strong small soft loop transfer space at the identity element. This indicates that the soft quasitopological fundamental group of a soft connected and locally soft path connected space, is a soft topological group.

Some Properties on Soft Simply Star Open Sets in Soft Topological Space

The present study aimed at introducing new topological concepts at soft spaces based on a class of soft simply star open set namely, soft-simply star boundary, soft simply star exterior soft-simply star limit point, and soft simply star neighborhood of a point. The study investigated some of their properties where notions can be applied in many applications in different fields, for example in medicine, engineering, and economics.

Ultrasonography versus conventional methods (Mallampati score and thyromental distance) for prediction of difficult airway in adult patients

ABSTRACT Background The poor reliability of traditional screening tools to identify a potentially difficult airway makes the difficult laryngoscopy and tracheal intubation rate remains at 1.5–13%.The hypothesis is that fat pads affect the view during direct laryngoscopy so the increasing thickness of pretracheal soft tissue or pre-epiglottic space could be strong predictors of difficult laryngoscopy as the mobility of the pharyngeal structures is impaired. Upon that, we aimed to evaluate ultrasound-measured distance from skin to epiglottis for prediction of difficult laryngoscopy in Egyptian population. Methods This was a prospective single blind randomized clinical study conducted on 80 patients requiring general anesthesia.Preoperatively, airway evaluation was performed using three parameters including Mallampati score, thyromental distance and ultrasound-measured distance from skin to epiglottis at the level of thyrohyoid membrane. The primary outcome was to correlate ultrasound measured distance from skin to epiglottis with difficult laryngoscopy in Egyptian population using Cormack – Lehane grading. Results Difficult laryngoscopy group displayed greater thickness of the ultrasound measured distance from the skin to epiglottis(2 ± 0.3 cm versus 1.7 ± 0.3 cm; p = 0.002). The cut-off point for difficult laryngoscopy was >1.85 cm with sensitivity of 80%, specificity of 70.8% and area under the receiver operating characteristic curve was 0.759. Mallampati score and thyromental distance had poor area under the curve = (0.651, 0.670 respectively). Conclusion Our study revealed good correlation between ultrasonograohic measurement of the skin to epiglottis distance and Cormack-Lehane grade in Egyptian population, therefore it might be considered as a predictor of difficult laryngoscopy. Clinical trial number NCT03799055.