Omega open sets in generalized topological spaces samer al ghour, wafa zareer department of mathematics and statistics, jordan university of science and technology, irbid 22110, jordan. On generalized topological spaces artur piekosz abstract arxiv. Suppose h is a subset of x such that f h is closed where h denotes the closure of h. Roy and erdal ekici, on, closed sets in generalized topological spaces, method of functional analysis and topology, 172 2011, 174179. In this paper we study generalized closed sets in the sense of n. We introduce the notion of generalized topological space gtspace. Jeyaraman, 1 assistant professor, department of mathematics, rdm government arts college, sivagangai. In the present work, a new class of sets called soft gclosed sets in soft topological spaces is introduced and some of their properties are studied. Supra generalized locally closed sets in this section, we introduce the notions of supra generalized locally closed sets and discuss some of their properties. Nano generalized locally closed sets and nglccontinuous functions in nano topological spaces 1. Minimal open sets on generalized topological space scielo. T h e n t h e f o l l o w i n gs t a t e m e n t sh o l d. Nano generalized locally closed sets and nglccontinuous. Abstract in this paper we introduce a new class of sets namely, gs closed sets, properties of this set are investigated and we.

Generalized topology of gtspace has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. Dontchev and maki have introduced the concept of generalized closed sets, in 1997 park et. A new class of locally closed sets and locally closed. Sets and the associated closure operator, the special issue in. The concepts of minimal open sets and maximal closed sets in topolog. Some generalizations of locally closed sets iranian journal of. This new class of sets widens the scope to do further research in the areas like bitopological spaces, smooth topological spaces and fuzzy soft topological spaces. Using generalized closed sets, dunham8 introduced the concept of the closure operator cl and a new topology and studied some of their properties. On semi star generalized closed sets in bitopological spaces key. R, pg student, nirmala college for women, coimbatore,tamil nadu. If the inline pdf is not rendering correctly, you can download the pdf file here.

Maki 12 introduced the notion of sets in topological spaces. The aim of this work is to introduce operations on fuzzy topological spaces and to use them to study fuzzy generalized closed sets and fuzzy generalized open sets. Pdf locally gclosed sets in topological spaces researchgate. Some of their properties and characterizations are studied. Finally we show that certain results of several publications on the concepts of weakness and strength of fuzzy generalized closed sets are. Decomposition of j closed sets in bigeneralized topo. A new class of generalized closed sets in topological spaces. In this paper weconsider a new class of generalized continuous. Generalized closed sets in generalized topological spaces 1m. J locally closed sets in bigeneralized topological spaces and study some of their properties. In this paper we have introduced the concept of regular.

In this paper another generalization of igclosed sets namely g i eclosed set is defined using semipre local function. Full text of on some locally closed sets and spaces in. Andrijevic 1996 introduced a class of generalized open sets in a topological space called bopen sets. A set is a set a which is equal to its kernel saturated set, i. The collection of all locally closed sets of x, will be. L, assistant professor, nirmala college for women, coimbatore, tamil nadu. Arts college, udumalpet, tamilnadu, india 2department of mathematics, psgr krishnammal college for women, coimbatore, tamilnadu, india abstract.

Decomposition of closed sets in supra topological spaces. The aim of this paper is to introduce a new class of sets called delta generalized. Decomposition of closed sets in supra topological spaces s. We define and study regular and locally closed sets in generalized topological spaces.

The aim of this paper is to introduce and study a new class of generalized closed sets called gp closed sets in topological spaces using gp closed sets. This type of set was investigated by ekici and caldas 2004 under the name of jopen sets. In 1970, levine studied the concept of generalized closed sets and a class of topological spaces called t 12 space. Introduction to generalized topological spaces zvina. In 1970, levine9 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. Levine 16 initiated the study of socalled generalized closed sets. Regular weakly generalized locally closed sets in ideal topological spaces 1s. Steiner 5 gave a new type of generalized closed set in topological space called generalized b closed sets and study some of its fundamental properties. Paper 1, section ii 12e metric and topological spaces. Reily 6 introduced and studied different notions of generalized continuity and gave a decomposition. Nagaveni2 1,2 department of mathematics, coimbatore institute of technology, india abstract. Some weaker forms of decompositions in supra topological. Regular weakly generalized locally closed sets in ideal. On generalized closed sets in generalized topological spaces.

According to bourbaki a subset of a topological space is locally closed if it is the intersection of an open set and a closed set. Ais a family of sets in cindexed by some index set a,then a o c. On generalized closed sets in generalized topological. Introduction and preliminaries norman levine introduced and studied generalized closed briefly gclosed sets 11 and semiopen sets 12. Using generalized closed sets, dunham 1982 introduced the concept of generalized closure operator cl and obtained a class of topology, namely topology. Generalized closed sets in fuzzy topological spaces 35 proposition 3. For a subset a of x, the closure of a and the interior of a will. Informally, 3 and 4 say, respectively, that cis closed under. Generalized topological spaces and generalized open sets play a very impor.

Navaneethakrishnan and others published generalized locally closed sets in ideal topological spaces find, read and cite all the research you need on researchgate. We also study the concept of generalizations of jlocally closed set in bgts. Vaidyanathaswamy 10 was given much importance to the topic and ideal topological space. A is a family of generalized topologies on a set x.

Also, we introduce some characterizations and properties for these concepts. Chapter 9 the topology of metric spaces uci mathematics. Regular sets in generalized topological spaces authors. Meena priyadarshini 1department of mathematics, kumaraguru college of technology, coimbatore, tamil nadu, india e mail. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. The approach of the concept of semiregularization from a different perspective via the. Also it is shown that the class of mclosed sets is independent from the class of preclosed setsthe class of generalized closed setsthe class of g. Knebusch and their strictly continuous mappings begins. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college. In this paper, we introduce a new class of sets called supra locally closed sets and new class of maps called supra locally continuous functions. Also we discuss some of their properties and investigate the relations between the associated.

Rajarubi abstract in this paper, we introduce a new class of sets called. Lo 12 jun 2009 in this paper a systematic study of the category gts of generalized topological spaces in the sense of h. Closed sets are fundamental objects in a topological space. Remind that each constructible set is a finite union of locally closed sets. Pdf generalized locally closed sets in ideal topological. Saadati abstract we extend the notion of omega open set in ordinary topological spaces to generalized topological spaces. We investigate various classes of generalized closed fuzzy sets in topological spaces, namely, closed fuzzy sets and closed fuzzy sets. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy. Balachandran, sundaram and maki 1 introduced and investigated the concept of generalized locally closed sets. On generalized topological spaces pdf free download. Navaneethakrishnan and sivaraj 7 were introduced the concept of iglocallyclosed sets in ideal topological spaces. Alexandrov topology the topology of a space x is an alexandrov topology or is finitely generated if arbitrary intersections of open sets in x are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of a poset.

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