Semiregular Space Research Articles

Semi-separation axioms associated with the Alexandroff compactification of the $ MW $-topological plane

<abstract><p>The present paper aims to investigate some semi-separation axioms relating to the Alexandroff one point compactification (Alexandroff compactification, for short) of the digital plane with the Marcus-Wyse ($ MW $-, for brevity) topology. The Alexandroff compactification of the $ MW $-topological plane is called the infinite $ MW $-topological sphere up to homeomorphism. We first prove that under the $ MW $-topology on $ {\mathbb Z}^2 $ the connectedness of $ X(\subset {\mathbb Z}^2) $ with $ X^\sharp\geq 2 $ implies the semi-openness of $ X $. Besides, for the infinite $ MW $-topological sphere, we introduce a new condition for the hereditary property of the compactness of it. In addition, we investigate some conditions preserving the semi-openness or semi-closedness of a subset of the $ MW $-topological plane in the process of an Alexandroff compactification. Finally, we prove that the infinite $ MW $-topological sphere is a semi-regular space; thus, it is a semi-$ T_3 $-space because it is a semi-$ T_1 $-space. Hence we finally conclude that an Alexandroff compactification of the $ MW $-topological plane preserves the semi-$ T_3 $ separation axiom.</p></abstract>

Neutrosophic soft semi-regularization and neutrosophic soft sub-maximality

In this study, our target point is to focus on neutrosophic soft semi-regularization spaces connected with neutrosophic soft topological spaces and examine their properties. First, we define the neutrosophic soft sub-maximal space and present the evidences for the existence of a neutrosophic soft sub-maximal space for every neutrosophic soft topological space. In this document, we focused on the relationship of neutrosophic soft sub-maximal spaces and neutrosophic soft semi-regular spaces with these spaces. Also, we find that this relationship is very close and it is minimal or maximal depending on some definite properties which are called neutrosophic soft semi-regular properties. This led us to examine the semi-regularity of different properties. After all, we introduced some types of functions in neutrosophic soft topological spaces that correspond with some types of functions previously defined in many topological spaces of different types and revealed the behaviours of these functions according to the cases where their domain or codomain spaces are replaced by their semi-regularization spaces.

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.

On Fuzzy Semi Regular Volterra Spaces

In this paper, the notion of semi regular Volterra spaces in fuzzy setting is introduced. Some characterizations of fuzzy semi regular Volterra spaces are also studied in this paper.

Semi Regular and semi weak Regular spaces in intuitionistic topological spaces

Semi Regular and semi weak Regular spaces in intuitionistic topological spaces

English

We introduce the cardinal invariant $\theta $-$aL'(X)$, related to $\theta $-$aL(X)$, and show that if $X$ is Urysohn, then $|X|\leq 2^{\theta \text {-}aL'(X)\chi (X)}$. As $\theta $-$aL'(X)\leq aL(X)$, this represents an improvement of the Bella-Cammaroto inequality. \endgraf We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly $H$-closed spaces, related to $H$-closed spaces.

On Minimal and Maximal Regular Open Sets

The purpose of this paper is to investigate the concepts of minimal and maximal regular open sets and their relations with minimal and maximal open sets. We study several properties of such concepts in a semi-regular space. It is mainly shown that if X is a semi-regular space, then miO(X) = miRO(X). We introduce and study new type of sets called minimal regular generalized closed. A special interest type of topological space called rTmin space is studied and obtain some of its basic properties.

On Irresolute Topological Vector Spaces-II

In this paper, we continue the study of Irresolute topological vector spaces. Notions of convex, bounded and balanced set are introduced and studied for Irresolute topological vector spaces. Along with other results, it is proved that: 1. Irresolute topological vector spaces are semi-Hausdorff spaces. 2. Every Irresolute topological vector space is semi-regular space. 3. In Irresolute topological vector spaces, as well as is convex if is convex. 4. In Irresolute topological vector spaces, is bouned if is bounded. 5. In Irresolute topological vector spaces, is balanced if is balanced and 6. In Irresolute topological vector spaces, every semi compact set is bounded.

Further Inquiry of Semi-Separation Axioms

In this paper, we introduce inclusive completely semi-regular space in L-fuzzy topology spaces and discuss some of its properties. Then, we introduce semi-homeomorphism and show inclusive completely semi-regular space is preserved under semi-homeomorphism.

Semi Regular and semi weak Regular spaces in intuitionistic topological spaces

The aim of this paper, giving a new definition of semi-Regular and semi weak Regular spaces inIntuitionistic topological space in additional to studying some correlated equation with several example.

A NEW TOPOLOGY FROM AN OLD ONE

In the present paper we construct and introduce a new topology from an old one which are independent each of the other. The members of this topology are called <TEX>${\omega}_{\delta}$</TEX>-open sets. We investigate some basic properties and their relationships with some other types of sets. Furthermore, a new characterization of regular and semi-regular spaces are obtained. Also, we introduce and study some new types of continuity, and we obtain decompositions of some types of continuity.

Semi-Generalized Closed Mappings and Generalized-Semi Closed Mappings and Its Relationships with Semi-Normal and Semi-Regular Spaces

In this paper, the semi-generalized closed maps (sg-closed maps) and generalized semi-closed maps (gs-closed maps) are studied and some results are presented and proved including the study of some of their basic properties which are related to such type of mappings. Also, a study of s-normal spaces and s-regular spaces is given using its relationships with sg-closed and gs-closed mappings.

SOME TYPES OF COMPLETELY REGULAR SPACE AND IT’S RELATIONS

In this paper , we introduced a new definitions of semi completely regular space and semi regular space . And we study some relations among the( s , g , s g, g s , g* , s g* , g*s )of completely regular spaces

Almost Perfectly Continuous Functions

The aim of the present paper is to continue the study of almost perfectly continuous (≡ regular set connected) functions initiated by Dontchev, Ganster and Reilly. It turns out that in general the notion of almost perfectly continuity is independent of continuity but represents a significantly strong form of continuity called ‘cl-supercontinuity’, if Y is a semiregular space. Basic properties of almost perfectly continuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the literature is discussed. Moreover, suffcient conditions on X and Y are outlined for the function space of all almost perfectly continuous functions from X to Y to be closed in YX with the topology of pointwise convergence.

S-expandable spaces

We introduce the concept of s-expandable spaces as a variation of expandable spaces. We show that an extremally disconnected semi-regular space is s-expandable if and only if it is expandable.

θ-Connectedness and δ-connectedness in fuzzy bitopological spaces

In this paper we introduce the concepts of θ-connectedness and δ-connectedness with the help of quasi coincidence due to Pu and Liu [6] for fuzzy sets in fuzzy bitopological setting as a weaker version of connectedness. In particular, we investigate their properties in almost regular, semi-regular and regular spaces, their invariants and preservations under mappings.

Fuzzy semiregularization topologies and fuzzy submaximal spaces

Abstract The aim of the paper is to investigate the fuzzy semiregularization spaces associated with fuzzy topological spaces. The concept of fuzzy submaximal spaces is introduced and it is proved that corresponding to every fuzzy topological space, there always exists a fuzzy submaximal space which is an expansion of the given space. Fuzzy submaximal and semiregular spaces are shown to be closely associated with those spaces which are minimal or maximal with respect to certain types of properties which we call fuzzy semiregular properties. This has induced us to take up different properties for investigation whether these are fuzzy semiregular ones. Lastly we consider certain mappings between fuzzy topological spaces and study their behaviour when either or both the domain and codomain spaces are replaced by their semiregulatization spaces.

Accumulation points of nowhere dense sets in $H$-closed spaces

In this paper a ten year old problem by Kulpa and Szymanski is settled by constructing an example of a minimal Hausdorff space without isolated points which has a point that is not the accumulation point of any nowhere dense subset of the minimal Hausdorff space. Also, a result by Kulpa and Szymanski is extended by showing that a regular point in an H-closed space without isolated points is the accumulation point of some nowhere dense subset. A decade ago, Kulpa and Szymafnski [KS] showed that each point in a compact Hausdorff space without isolated points is the accumulation point of a nowhere dense set and they asked if the result is true in the setting of minimal Hausdorff spaces without isolated points. They noted that the result is false for arbitrary H-closed spaces without isolated points. In this paper, we settle this question by giving an example of a minimal Hausdorff space without isolated points and a point which is not the accumulation point of any nowhere dense set. Also, we extend Kulpa and Szymanski's result by showing that a regular point in an H-closed space without isolated points is the accumulation point of some nowhere dense subset. First, a few preliminary results and definitions are needed. All spaces considered in this paper are assumed to be Hausdorff. A space X is H-closed if X is closed in every space in which X is a subspace. An open set U in a space X is said to be regular open if U = int(cl U). A space X is semiregular if { U c X: U is regular open} is a base for the topology of X and is minimal Hausdorff if there is no strictly coarser Hausdorff topology on the space. Katetov [K] has shown that a space is minimal Hausdorff iff it is H-closed and semiregular. For a space X, let tX = X U {q: qi is a free open ultrafilter on X}. For each open set U c X, let oU= U U { E It X\X: int(clV) c U for some Ve 9/}. THEOREM 1. Let X be a semiregular space. The following are true: (a) [B, F, S] The family {oU: U is regular open in X} is a base for a minimal Hausdorff extension ttX of X. (b) [PW] For a regular open subset U of X, cl,,XoU = oU U cl xU. D Received by the editors May 29, 1984. 1980 Mathematics Subject Classification. Primary 54D25.

On Regular-Invariance of Continuity

Let $(X,\sigma )$ be a given topological space. A compression $\tau$ of $\sigma$ is regular-invariant if and only if for every regular space $Y$ the $\sigma$-continuous functions into $Y$ are also $\tau$-continuous. $\sigma$ is regular minimal if no proper compression of $\sigma$ is regular-invariant. J. A. Guthrie and H. E. Stone posed the problem of whether every semiregular space is regular minimal. We answer this question in the negative.

Embeddings in Minimal Hausdorff Spaces

We show that not every semiregular space is embeddable as an open and dense set of some minimal Hausdorff space. Also a space is constructed for which it is not decidable in Z.F.C whether such an embedding exists.