College of engineering and technology, pollachi642 002. Namely, we will discuss metric spaces, open sets, and closed sets. In this research paper, a new type of closed sets called generalization of generalized closed sets gg closed sets are introduced and studied in a topological space x. In w 2 we shall define generalized closed written henceforth as gclosed sets and characterize them as. Chaudhary and others published on gclosed sets in a topological space find, read and cite all the research you. In this paper, the authors introduce and study the concept of a new class of closed sets called weakly generalized e. In this paper another generalization of igclosed sets namely g i eclosed set is defined using semipre local function. Using generalized closed sets, dunham 1982 introduced. Indira2 1,2pg and research department of mathematics, seethalakshmi ramaswamy college autonomous, trichirapalli620002, india abstract. The aim of this paper is to continue the study of gp closed sets thereby contributing new innovations and concepts in the field of topology through analytical as well as research works. The aim of this paper is to introduce and study a new class of generalized closed sets called gpclosed sets in topological spaces using gpclosed sets. The aim of this paper is to introduce a new class of sets namely rg closed sets in topological spaces. We have introduced and investigated concept of fuzzy strongly gclosed set and proved some properties with some examples the way they are related to. A regular generalized closed set briefly rgclosed if cla.
The open and closed sets of a topological space examples 1. In this article, the notion of neutrosophic bg closed sets in. A subset a of x is said to be b g closed if bcla u whenever a u and u is g open in x. In this paper, aspects of generalized continuity and generalized closedness are explored. A subset a of a topological space x,t is called a semi generalized. Also we discuss some of their properties and investigate the relations between the associated. Pushpalatha department of mathematics, government arts college udumalpet642126, tirupur district tamilnadu, india r. International journal of mathematics trends and technology. Pdf on gclosed sets in a topological space researchgate.
Paper open access neutrosophic generalized b closed. Introduction in this chapter we introduce the idea of connectedness. A connected space need not\ have any of the other topological properties we have discussed so far. Parimelazhagan2 1research scholar,karpagam university,india 2department of science and humanities, karpagam college of engineering, anna university, india abstract.
Sheik john et al 14 introduced gclosed sets in bitopological spaces. Strongly g closed sets in topological spaces 1 introduction mhikari. The purpose of the present paper is to define a new class of closed sets called i, j. L, assistant professor, nirmala college for women, coimbatore, tamil nadu. Pdf on nov 8, 2018, govindappa navalagi and others published properties of gclosed sets in topological spaces find. Pdf the notion of gclosed sets is introduced in ideal topological spaces. Ais a family of sets in cindexed by some index set a,then a o c. In this paper, we studied the fuzzy topological spaces after giving the fundamental definitions. Union of two gclosed sets in x is a gclosed set in x. In this paper, we obtain a new generalization of closed sets in the weaker topological space x. Applying these sets, we obtain a new space which is called t 34space.
In this case, the spaces xand yare called equivalent, or homeomorphic. The notion of gclosed sets is introduced in ideal topological spaces. The converse of the above theorem need not be true, as seen from the following example. Indeed ideals are very important tools in general topology. Generalized closed sets and open sets in topological spaces. If a is strongly g closed and a is open then a is g closed set. Nithyakala department of mathematics vidyasagar college of arts and science udumalpet, tirupur district tamilnadu india abstract. A subset a of a generalized topological space we recall some notion defined in 1, 2. If x is a topological space and x 2 x, show that there is a connected subspace k x of x so that if s is any other connected subspace containing x then s k x. Y is an equivalence, or homeomorphism, if there exists a continuous function g.
Semi \cs\generalized closed sets in topological spaces in this paper, we have introduced a new class of closed set, as a weaker form of closed set namely semi \cs\generalized closed set in topological space. On generalized gp closed set in topological spaces. The notion of generalized closed sets in ideal topological spaces was studied by dontchev et. Characterizations and properties of igclosed sets and igopen sets are. The main aim of this paper is to introduce some new related closed sets in the same space and study. Generalized closed sets with respect to an ideal european. An alternative characterization of closed sets is available via sequences and nets. Chapter 5 compactness compactness is the generalization to topological spaces of the property of closed and bounded subsets of the real line. Connectedness is a topological property quite different from any property we considered in chapters 14. In this paper a class of sets called g closed sets and g open sets and a class of maps in topological spaces is introduced and some of its properties are discussed. In this paper introduced q g closed sets in supra topological space. While compact may infer small size, this is not true in general. Rajendra kumar and anandajothi 9 accordingly, the proposed study is to introduce a new class of fuzzy soft closed sets namely fuzzy soft generalized closed. The notion of closed set is defined above in terms of open sets, a concept that makes sense for topological spaces, as well as for other spaces that carry topological structures, such as metric spaces, differentiable manifolds, uniform spaces, and gauge spaces.
Veera kumar 3 introduced the study of iclosed, dclosed and bclosed sets in 2001. A new class of generalized closed sets in topological spaces. We also investigate several properties of such sets. Rajarubi abstract in this paper, we introduce a new class of sets called. Closed sets are fundamental objects in a topological space. The aim of this paper is to introduce and study a new class of generalized closed sets called g p closed sets in topological spaces using gpclosed sets. If a and b are g closed sets in a topological space x, then a b is. Metricandtopologicalspaces university of cambridge. The standard material on the notions of g open, g open sets and some definitions and results that are needed are presented first. Abstract in this paper we introduce a new class of sets namely, gsclosed sets, properties of this set are investigated and we. Characterizations of prer0 and prer1 topological spaces.
On generalized closed sets in generalized topological. Further closed sets like i rg,i rw were further developed by navaneethakrishnan 10 and a. Miguel caldas, saeid jafari, takashi noiri comments. R, pg student, nirmala college for women, coimbatore,tamil nadu. Semi \cs\generalized closed sets in topological spaces. Characterizations and properties of i gclosed sets and i gopen sets are given. Pdf gclosed sets in intuitionistic fuzzy topological. Informally, 3 and 4 say, respectively, that cis closed under. In this paper we introduce two new classes of topological spaces called prer0 and prer1 spaces in terms of the concept of preopen sets and investigate some of their fundamental properties.
Throughout this paper x and y are topological spaces on which no separation axioms are. The open and closed sets of a topological space examples 1 fold unfold. Y between topological spaces is continuous if and only if the inverse image of every closed set is closed. A subset a of a space x is called a delta generalized. More informally, ii and iii state that intersections and finite unions of closed sets are closed. Suppose that fis continuous and let a y be a closed set. Generalized closed sets in topological spaces iaeng. Vaidyanathaswamy, the localization theory in settopology, proceedings of the indian academy of science, 20 1945, 5160. Applications of gspclosed sets in topological spaces govindappa navalagi1. In this paper we introduce and study a new class of generalised closed sets called. The notion of q closed sets in a topological spaces was introduced by murugalingam and lalitha4 in 2010. In this paper, we have introduced a new class of sets called b g closed sets in topological spaces.
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