Bitopological spaces pdf
Dvalishvili, Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications (Elsevier/North Holland, 2005). the systematic study of such spaces and several other authors have contributed to the development of the theory.
spaces that is in terms of open (or closed) sets.if the concept was defined in topological terms ß This applies, for example, to the definitions of interior, closure, and frontier in pseudometric spaces, so these definitions can also be carried over verbatim to a topological space Ð\ß ÑÞg Definition 2.7 Suppose . Further we introduce and study bĝ–Neighbouhood, –bĝ–Continuous maps and Pair wise bĝ– irresolute maps. In this paper, we shall continue the study of pairwise Lindel¨of bitopological spaces initiated by Fora and Hdeib.
Pokhariyal, Separation axioms on functional spaces defined on bitopological spaces, Journal of Advanced Studies in Topology, Vol. There are several kinds of fuzzy set extensions in the fuzzy set theory, for example, intuitionistic fuzzy set, vague fuzzy set, interval-valued fuzzy sets, etc. bitopological spaces is a generalization of the study of fuzzy soft topological spaces. Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications: Theory, Relations with Generalized Algebraic Structures and Applications by Dvalishvili, Badri and Publisher North Holland. A family A of subsets of a bitopological space X = (X;˝1;˝2) is called p- locally-a family, if for all x 2 X there exists a ˝1 open set U containing x such that U meets less than a members of A\˝2 or there exists a ˝2 open set V containing x such that V meets less than a members of A\˝1.
The main tool is a Stone-type duality between the category of d-frames, which was developed by Jung and Moshier, and bitopological spaces. This concept helps the authors to generalize the most results related to the topological spaces, which are known before. We shall give some results concerning these bitopological spaces and their relations. The notion of ideal in topological spaces was studied by Kuratowski  and Vaidyanathaswamy . This thesis consists of two parts; the rst part is the study of ideal topological spaces. Save up to 80% by choosing the eTextbook option for ISBN: 9780444517937, 9780080459462, 0080459463. The product of two soft (S:=1,2) axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced.
Stone duality for bitopological spaces Without spending too much time on motivation, we now sketch a Stone duality for bitopological spaces; for the full picture we refer to . In this paper, using bitopological semi-open sets, an asymmetric generalization of Haworth-McCoy's well-known theorem [4, Theorem 3.1] about Baire spaces is established. Also, he introduced generalized closed sets and pairwise generalized closure operator 9 in bitopological spaces in 1986. Several prop-erties of almost upper (lower) nearly quasi-continuous and almost nearly quasi-continuous multifunctions have been obtained. In a similar way, Sheik John  introduced the classes of Z-regular and Z-normal spaces using the class of Z -closed sets in topological spaces. Some applications are given to the hyperspace operator introduced in an earlier paper. The study of bitopological spaces was initiated by Kelly  and thereafter a large number of papers have been done to generalize the topological concepts to bitopological setting. bitopological spaces then study the relations between those classes and some properties .
In addition, various examples and counterexamples are given for answers to some questions raised in this study. bitopological spaces, while in the category of locales every locale comes equipped with a natural internal topology. The concept of continuity in topological spaces was extended to bitopological spaces by Pervin . Other aim is to introduce certain type of connectedness in bitopological spaces relative to the new classes of sets introduced in the first part, and get some results . amir barhoi* pdf • existence of solution of riemann-liouville fractional differential equations involving the sum of two functions.
The aim of this work is to introduce some weak forms of continuity in bitopological spaces. Especially, gen-eralized continuity admits a characterization furnishing a known characterization of -continuous maps. In 1979, Kasahara , introduced the concept of operations on topological spaces.
Keywords: Fuzzy bitopological spaces, fuzzy regular open sets, fuzzy continuous mappings, fuzzy almost continuous mappings, fuzzy weakly continuous mappings. We study the notions of pairwise *-connected ideal bitopological spaces, pairwise *-separated sets, pairwise *s-connected sets and pairwise *-connected sets in ideal bitopological spaces. bitopological spaces over B, by the first projection and in the same way for every subspace of . Morphisms between bitopological spaces are required to be continuous with respect to each of the two topologies; this gives rise to the category biTop. The author hopes that from now on generalized topology (hidden in the language of locally semialgebraic spaces of , and weakly semialgebraic spaces of ) will be developed without constraints.
In 1989, KANDIL  introduced the concept of fuzzy bitopological spaces as a generalization of fuzzy topological spaces. We also study strongly zero-dimensional ordered topological spaces and their relation with functorial quasi-uniformities. In this present study, we discuss soft-gsr-closed sets in soft bitopological spaces and their properties. The aim of this article is to associate a bitopological space with every locally finite graph G (a graph in which every vertex is adjacent with finite number of edges). Every metric space can be given a metric topology, in which the basic open sets are open balls defined by the metric. This thesis extends the concept of compactiﬁcations of topological spaces to a setting where spaces carry a partial order and maps are order-preserving. Some Modifications of Baire-Like Properties 152 CHAPTER V Dynamics of Bitopological Relations, Baire-Like Properties and Dimensions 5.1.
We continue the study of bitopological separation axioms that was begun by Kelly and obtain some results. This work is licensed under a Creative Commons Attribution 4.0 International License. After Kelly’s initiation of the bitopological notion, many authors generalized many topological concepts to include bitopological spaces.
Bitopological spaces were introduced by Kelly  in 1963 as an extension of topological spaces. In this paper we continue previous investigations on the weaker forms of the Menger property in bitopological spaces. the order is important (i.e., two bitopological spaces (X,t,g) and (X,t0,g0) are identical if, and only if, t = t0and g = g0). Purchase Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications, Volume 199 - 1st Edition. Sheik John and Sundaram  introduced g*- closed sets and g*-continuity in bitopological spaces in 2002.
By using this set we introduce the notion of Si-continuity and investigate some of its properties. In particular, Menger type, and Hurewicz type covering properties like: Almost p-Menger, star p-Menger, strongly star p-Menger, weakly p-Hurewicz, almost p-Hurewicz, star p-Hurewicz and strongly star p-Hurewicz spaces are defined and corresponding properties are investigated. Srivastava, On certain separation axioms in fuzzy bitopological spaces, Far East Journal of Math. Fukutake  introduced and studied the notions of generalized closed sets in bitopological spaces. In this paper, introduce and study the concept of soft bitopological spaces which are defined over an initial universe with a fixed set of parameters. Since then several topologists generalized many of the results in topological spaces to bitopological spaces. Bitopological spaces , and based on this we introduc e some related definition s and theorem s about P closed set and open sets .
the expected price and the original price of a commodity with the help of local functions and expansion operators of a bitopological space. disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. Space(M) of spaces over a weakly topological M, and ﬁnite completeness of its full subcategories ADS(M), DS(M), LDS(M), WDS1(M). Ittanagi  deﬁned the notion of soft bitopological space and gave some of types of soft separation axioms.
Bitopological spaces were introduced in Kelly (1963) for the study of quasi-metric spaces. Quasi-uniform spaces, which are generalizations of quasi-metric spaces, also induce bitopological spaces. The paper is, in essence, a monograph devoted to the theory of bitopological spaces and its applications. Also, the class of (i;j)-bI-countably com-pact spaces is introduced with some of its properties. On Semi -regular Pre-Semi Closed Sets In Bitopological Spaces In this section, we introduce the concept of ˝ 1˝ 2-s rps-closed sets in bitopological spaces and discuss some of the related properties. In this paper the concepts of Pairwise S**GLC – continuous, Pairwise S**GLC – irresolute are introduced and study their basic properties.
The notions of ˝-smooth closure and ˝-smooth interior were given in .
INTRODUCTION AND PRELIMINARIES Let be a topological space, a subset of is said to be a discrete set if the subspace is discrete space, i.e., is discrete set in if for each point , there is an open set in containing , s.t. of a bitopological space and a group of all nqs-homeomorphisms which are invariant on a subspace. Unlimited viewing of the article/chapter PDF and any associated supplements and figures.
Focussing on complete regularity, we discuss the separation properties of bitopological spaces. INTRODUCTION Fuzzy topological spaces have been developed as an extension of the classical point-set topological spaces.
Jankovic and Hamlet have introduced the notion of I-open sets in topological spaces. tween the category of intuitionistic topological spaces and continuous mappings and the category of bitopological spaces and pairwise con-tinuous mappings. We also use these concepts to introduce the new notions of some operator as well as ij-generalized semi-closure, ij-semi-generalized closure, ij-generalized semi-interior and ij-semi-generalized interior. bitopological spaces and their algebraic counterparts, called d-frames, covers several of the known dualities such as Stone duality, Priestley duality, and the duality of topological spaces and frames. Saeid Jafari and Takashi Noiri On faintly -continuous functions 203-210 Abstract: Long and Herrington  introduced and investigated the notion of faint continuity.
Kandil  introduced the concept of fuzzy bitopological space as an extension of fuzzy topological space and as a generalization of bitopological space. Journal of Mathematics is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics. A non-empty set X equipped with two topologies and called a bitopological spaces. Not exhausting the entire subject, it reflects basic ideas and methods of the theory. The purpose of this paper is to introduce and study (i,j)*- extremally disconnected ideal bitopological space.
Also, two supra bitopological spaces S˝ ij-T 1/2 and S˝ ij-T 1/2-spaces are introduced. We publish over 180 high-quality full open access journals, ranging across disciplines and subject areas. An almost nearly continuity and almost nearly quasi-continuity have been investigated in a bitopological case. We introduce the notions of homogeneous and pairwise homogeneous fuzzy bitopological spaces. The notion of connectedness in bitopological spaces has been studied by Pervin, Reily and Swart.
Das  initiated the study of semi connectedness in topological spaces and Dorsett  continued the study of the same further. Thampuran, with 2 highly influential citations and 13 scientific research papers. But nding the examples for such generalized closed sets to support the results are very di cult as well as time taken process. The inter-relations between pair-wise fuzzy semi Volterra and pairwise fuzzy semi weakly Volterra spaces, are also established. Introduction Mathematical problems become more challenging if uncertainty is involved.