Punctured Plane Research Articles

Several generalizations of Is*g -Continuous Functions in Ideal Topological Spaces

Khan and Noiri( Khan M. and Noiri T., On Is*g -continuous functions in the Ideal Topological spaces, Eur. J. Pure Appl. Math., 4(3)(2011), 237 – 243.) have initiated the notion of Is*g -continuous functions in ideal Topological spaces. In addition to this, they have also defined the strong and weak versions of Is*g -continuous functions along with their mutual relationships and studied certain properties of these functions. By considering the definition of β-open sets, the authors have proposed the generalization of Is*g -continuous functions viz. Is*g -β-continuous functions in the present paper. Moreover, the generalization of weak I-continuous functions and weakly Is*g -continuous functions have been defined in the context of β-open and regular open sets. The relationships amongst these continuities have been also established and the generalization has been justified by several illustrative examples.

Some separation axioms in soft ideal topological spaces

Abstract For dealing with uncertainties researchers introduced the concept of soft sets. In this paper, a new class of soft sets called soft delta pre ideal open sets in soft ideal topological space related to the notion of soft pre ideal regular pre ideal open sets is introduced. Also, some new soft separation axioms based on the soft delta pre ideal open sets are investigated.

Fuzzy regular open sets via operations

The aim of this paper is to introduce and study the concepts of r-fuzzy γ-regular open sets and their related notions in topological spaces.

WEAKLY (1,2)$^{\ast}$-$\widetilde{g}$-CLOSED SETS IN BIOTOPOLOGICAL SPACES

The concept of bitopological spaces was first introduced by J.C. Kelly [2] in 1963. Regular open sets have been introduced and investigated by Stone [5]. In this paper, we introduce a new class of generalized closed sets called weakly (1,2)$^{\ast}$-$\widetilde{g}$-closed sets which contains the above mentioned class. Also, we investigate the relationships among the related generalized closed sets.

On Almost $\alpha$-Topological Vector Spaces

The main objective of this paper is to introduce a new generalized form of topological vector spaces, namely, almost $\alpha$-topological vector spaces by using the concepts of $\alpha$-open sets, regular open sets, and almost $\alpha$-continuous mappings. In the present paper, some important examples of almost $\alpha$-topological vector spaces with basic properties are characterized.

Some New Properties of Fuzzy Maximal Regular Open Sets

A proper nonempty open subset of a fuzzy topological space is said to be a fuzzy maximal regular open set , if any regular open set which contains is or . The purpose of this paper is to study some new fundamental properties of fuzzy maximal regular open sets. The decomposition theorems for a fuzzy maximal regular open set are investigated. Notion and basic properties of radical of fuzzy maximal regular open sets are established, such as the law of fuzzy radical closure. Some new properties and characterization theorems of fuzzy maximal regular open set are achieved.

The lattices of families of regular sets in topological spaces

Abstract The question as to the number of sets obtainable from a given subset of a topological space using the operators derived by composing members of the set {b, i, ∨, ∧}, where b, i, ∨ and ∧ denote the closure operator, the interior operator, the binary operators corresponding to union and intersection, respectively, is called the Kuratowski {b, i, ∨, ∧}-problem. This problem has been solved independently by Sherman [21] and, Gardner and Jackson [13], where the resulting 34 plus identity operators were depicted in the Hasse diagram. In this paper we investigate the sets of fixed points of these operators. We show that there are at most 23 such families of subsets. Twelve of them are the topology, the family of all closed subsets plus, well known generalizations of open sets, plus the families of their complements. Each of the other 11 families forms a complete complemented lattice under the operations of join, meet and negation defined according to a uniform procedure. Two of them are the well known Boolean algebras formed by the regular open sets and regular closed sets, any of the others in general need not be a Boolean algebras.

Nano M Locally Closed Sets and Maps in Nano Topological Spaces

The concepts of sets, continuous and irresolute functions are introduced some of its characteristics are discussed. Also nano submaximal spaces are defined its properties are discussed.

Generalized regular open sets

Generalized regular open sets

Micropuncture Access Set Use During Implantation of Totally Implantable Venous Access Device May Reduce Upper Extremity DVT Incidence Among Patients Undergoing Chemotherapy for Colorectal Cancer.

The aim of this study was to compare the perioperative outcomes when using a micropuncture access set (MS) to those when using a conventional puncture set (CS) for implantation of totally implantable venous access device (TAVID). A total of 314 patients undergoing chemotherapy for colorectal cancer were included between June 2015 and July 2018. Of these, 123 (39.2%) received TAVID implantation using MS and 191 patients (60.8%) received TAVID using CS. Perioperative outcomes and complications were compared between both groups. Baseline characteristics, including body mass index, American Society of Anesthesiologists score, cardiovascular disease, diabetes mellitus, and hyperlipidemia, were not significantly different between the groups. Postoperative complications occurred in 25 patients (8.0%), and the rate and incidence of venous thrombosis were significantly higher in the CS group. There were no significant differences between the groups in other complications such as the rate of port site infection, deep vein thrombosis, obstruction, catheter dislocation, and skin complications (exposure). No incidence of catheter infection, port rotation, intraoperative bleeding, or pneumothorax was observed in this cohort. MS is a safe and feasible procedure and results in less thrombosis. MS may play an important role in improving outcomes for the implantation of TAVID.

CHOICE-FREE STONE DUALITY

AbstractThe standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras.

On nearly Lindelöf spaces via generalized topology

In this paper a new class of sets termed as ωμ-regular open sets has been introduced and some of its properties are studied. We have introduced μ-nearly Lindelofness in μ-spaces. We have shown that under certain conditions a μ-Lindelof space [7] is equivalent to a μ-nearly Lindelof space. Some properties of such spaces and some characterizations of such spaces in terms of ωμ -regular open sets are given.

Generalized Regular Fuzzy Irresolute Mappings and Their Applications

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open and generalized regular fuzzy irresolute closed maps in fuzzy topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy irresolute maps are investigated. As a natural follow-up of the study of r-generalized regular fuzzy open sets, the concept of r-generalized regular fuzzy connectedness of a fuzzy set is introduced and studied.

On RC-spaces

Following Frink’s characterization of completely regular spaces, we say that a regular T_1-space is an RC-space whenever the family of all regular open sets constitutes a regular normal base. Normal spaces are RC-spaces and there exist completely regular spaces which are not RC-spaces. So the question arises, which of the known examples of completely regular and not normal spaces are RC-spaces. We show that the Niemytzki plane and the Sorgenfrey plane are RC-spaces.

L-Almost separation axioms in L-fuzzifying-bitopologies via complete residuated lattice-valued logic

In this work, an extension of almost separation axioms is introduced in lattice valued theory. Such a generalized almost separation axioms is a structure of (i, j)-regular open set of its lattice-valued satisfying axioms. It uses two lattices one complete residuated lattice, and another strictly two-sided commutative quantale. It is a logical generalization of the notions of almost separation axioms. In our definition of generalized fuzzifying separation axioms, each notions can be regarded as relations between the one another to some degree.

∆*-Locally Continuous Functions and ∆*-Locally Irresolute Maps in Topological Spaces

The objective of the paper is to introduce a new types of continuous maps and irresolute functions called ∆*-locally continuous functions and ∆*-irresolute maps in topological spaces. The comparative study between these functions with other existing maps is discussed in this paper. Some significant results are also proved as an application of new spaces namely, ∆*-submaximal space and –space. Further the characteristics of these maps under composition maps are exhibited.

$$\gamma ^{*}$$γ∗-Hyperconnectedness in fuzzy topological spaces

This paper introduces the notion of \(\gamma ^{*}\)-hyperconnectedness in fuzzy topological space to show that it is completely independent to fuzzy hyperconnectedness in the sense of Miguel Caldas. The paper also presents some equivalence theorems linking the concept with regular open sets in this context. Applying this new effective idea we move forward one more step towards the difference between topological spaces and fuzzy topological spaces. We contemplate that this study may be applicable in parallel topology related to parallel circuit of electronic network and consequently in fuzzy graph theory also.

σ-Algebra and σ-Baire in Fuzzy Soft Setting

We first introduce some new notions of Baireness in fuzzy soft topological space (FSTS). Next, their characterizations and basic properties are investigated in this work. The notions of fuzzy soft dense, fuzzy soft nowhere dense, fuzzy soft meager, fuzzy soft second category, fuzzy soft residual, fuzzy soft Baire, fuzzy soft δ-sets, fuzzy soft λσ-sets, fuzzy soft σ-nowhere dense, fuzzy soft σ-meager, fuzzy soft σ-residual, fuzzy soft σ-Baire, fuzzy soft σ-second category, fuzzy soft σ-residual, fuzzy, fuzzy soft submaximal space, fuzzy soft P-space, fuzzy soft almost resolvable space, fuzzy soft hyperconnected space, fuzzy soft A-embedded, fuzzy soft D-Baire, fuzzy soft almost P-spaces, fuzzy soft Borel, and fuzzy soft σ-algebra are introduced. Furthermore, several examples are shown as well.

GENERALIZED TOPOLOGICAL APPROXIMATION SPACES AND THEIR MEDICAL APPLICATIONS

We generalize Pawlak's approximation space to topological approximation spaces using some topological near opensets, such as regular open sets, semi-open sets, pre-open sets,  -open sets,  -open sets and  -open sets and others. Theproperties of the topological approximations space will be studied. Finally, We applied our results on medical data.

In-clinic secondary tracheoesophageal puncture and voice prosthesis placement in laryngectomees

Secondary tracheoesophageal puncture (TEP) with voice prosthesis placement represents one of the possibility to restore vocal function after total laryngectomy. However, some patients have comorbidities that contraindicate general anesthesia. In our department, an in-clinic TEP procedure for retrograde voice prosthesis placement was developed. It allows the immediate placement of the prosthesis and the avoidance of the use of dilators. We described our technique with advantages and pitfalls. The Provox Vega Puncture Set was used. Our technique for in-clinic secondary TEP without general anesthesia or target controlled infusion was a safe and effective procedure. It allows the use of the traditional TEP set, with possibility of voice prosthesis placement after previous TEP closure.