A set is a set a which is equal to its kernel saturated set, i. Also, it is established that an i gclosed subset of an icompact space is icompact. The aim of this paper is to introduce a new class of sets namely rg closed sets in topological spaces. Maki 12 introduced the notion of sets in topological spaces. Evidently specifying the open subsets is equivalent to specfying the closed subsets. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. Open sets, closed sets, bases, and subbases chapter. In 2011, shabir and naz 14 initiated the study of soft topological spaces and. In the present paper we introduce and study the concept of irg closed sets in fuzzy ideal topological spaces. Some of the fundamental properties of this set are studied. We will provide characterizations of extremally disconnected spaces and sgsubmaximal spaces by using various kinds of generalized closed sets. In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. Y is the union of a countable sequence of rectangles u v with u and v open. In this paper, it will be shown that in ideal topological spaces, a set which is both closed set and semipre dense set is a.
The purpose of the present paper is to define a new class of closed sets called i,j grclosed sets and we discuss some basic properties of i,j grclosed sets in bitopological spaces. In this paper, we introduce a new class of closed sets which is called. Several specific types of generalized sets of a generalized topological space have been defined and investigated for various purposes from time. Pdf closed sets in topological spaces researchgate. Properties of soft semiopen and soft semiclosed sets arxiv. Pdf soft generalized closed sets in soft topological spaces. Certain new classes of generalized closed sets and their. Using generalized closed sets, dunham 1982 introduced the concept of. This class was obtained by generalizing closed sets via rg open sets which was introduced by n. The aim of this paper is to investigate the properties of these sets in the ideal topological spaces. Parimelazhagan2 1research scholar,karpagam university,india 2department of science and humanities, karpagam college of engineering, anna university, india abstract. Ali abbas1, shuker mahmood khalil2, 1ministry of education, baghdad, iraq 2department of mathematics, college of science, basra university, basra, iraq abstract in this work, we first introduce the concept of. We also investigate several properties of such sets.
We will consider the question of when some classes of generalized closed sets coincide. Because of this theorem one could define a topology on a space using closed sets instead of open sets. In the present paper, we introduce soft generalized closed sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters. As a continuation of this work, we introduce and study in section 3, a new class of sets namely gs closed sets which is properly placed in between the class of semiclosed sets and the class of gsclosed sets due to arya and nour.
On generalized closed sets in generalized topological. In 1997, fuzzy generalized closed set briefly was introduced by g. Regular generalized closed sets in fuzzy ideal topological. In this paper we have introduced a new class of sets called gspclosed sets which is properly placed in between the class of closed sets and gspclosed sets. In this paper, we have introduced a new class of sets called bgclosed sets in topological spaces. Applying these sets, we obtain a new space which is called t 34space. Nagaveni assistant pro fessor coimbatore institute of technology, coimbatore, india. Characterizations and properties of i gclosed sets and i gopen sets are given. Using generalized closed sets, dunham 1982 introduced the concept of generalized closure operator cl and. A regular generalized closed set briefly rgclosed if cla. Open sets, closed sets, bases, and subbases 1 chapter 11. For example, the various norms in rn, and the various metrics, generalize from the euclidean norm and euclidean distance. For any set x, we have a boolean algebra px of subsets of x, so this algebra of sets may be treated as a small category with inclusions as morphisms. Unlike in algebra where the inverse of a bijective homomorphism is always a homomorphism this does not hold for.
Knebusch and their strictly continuous mappings begins. Jeyaraman, 1 assistant professor, department of mathematics, rdm government arts college, sivagangai. Closed sets in neutrosophic topological spaces university of new mexico n. Between closed sets and closed sets in topological spaces. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college. On generalized closed sets in generalized topological spaces. Further, gspcontinuous, and gsp irresolute mappings are also introduced and investigated. Later on, jelic 9 extended their results to the bitopological setting by providing a decomposition of pairwise continuity and, quite recently, balachandran and sundaram studied several variations of lccontinuity in 5 and. Observe that an intersection of two regularly closed sets need not be regularly closed, for example, in.
In this paper, we have introduced a new class of sets called bg closed sets in topological spaces. One often says x is a topological space so mean that there is t such that x,t is a topological space. Generalized closed sets in generalized topological spaces 1m. The investigation on generalization of closed set has lead to significant contribution to the theory of separation axiom, generalization of continuity and irresolute functions. If a is strongly g closed and a is open then a is g closed set.
A characterization of normal spaces is given in terms of i gopen sets. The closed subsets of a topological space satsify the following properties. This new class falls strictly between the class of closed sets and rg closed sets. We investigate various classes of generalized closed fuzzy sets in topological spaces, namely, closed fuzzy sets and closed fuzzy sets. The closure of a set in a topological space examples 1. 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.
A subset a of x is said to be bg closed if bcla u whenever a u and u is gopen in x. Recently, many variations of gclosed sets are introduced and investigated. A subset of px is called generalized topology gt on x if is closed under arbitrary unions and in that case x, is called a generalized topological space. Topological spaces 29 assume now that t is a topology on xwhich contains all the balls and we prove that td. Further, we introduce the notions of interior, closure, boundary, exterior and study some of their properties. Topology and topological spaces mathematical spaces such as vector spaces, normed vector spaces banach spaces, and metric spaces are generalizations of ideas that are familiar in r or in rn.
A subset a of x is said to be bgclosed if bcla u whenever a u and u is gopen in x. As an application, we introduce two news paces namely, tgspspace, gtgspspace. In this setting, since we have a collection of open sets, we can still accomplish a study of the standard topics of. Meena priyadarshini 1department of mathematics, kumaraguru college of technology, coimbatore, tamil nadu, india e mail. Iopen sets 22 fuzzy ig closed, fuzzy ig open 17 sets have been introduced and studied in fuzzy ideal topological spaces.
Many researchers contributed towards the algebraic structures of soft set theory. A new class of locally closed sets and locally closed. In this paper, the authors introduce and study the concept of a new class of closed sets called weakly generalized e. A new class of locally closed sets and locally closed continuous functions in generalized topological spaces s. In 1994, maki, devi and balachandran introduced the class of. On the uniformization of sets in topological spaces. In 1970, levine 10 introduced the notion of generalized closed gclosed sets in topological spaces.
We will be providing unlimited waivers of publication charges for accepted articles related to covid19. This type of set was investigated by ekici and caldas 2004 under the name of jopen sets. We are committed to sharing findings related to covid19 as quickly and safely as possible. Rajarubi abstract in this paper, we introduce a new class of sets called. The notion of ideals in general topological spaces is treated in the classic text by kuratowski 4 and also in 10. Also, some lower separation axioms weaker than t 1 are investigated. American journal of mathematics and statistics 2018, 82. The elements of in this paper the idea of locally closed sets in. The authors introduce new type of closed set named gp closed set in the topological. Semi generalized bclosed sets in topological spaces 3. International journal of mathematics trends and technology.
On generalized topological spaces arturpiekosz abstract in this paper a systematic study of the category gtsof generalized topological spaces in the sense of h. On generalized gp closed set in topological spaces. On the uniformization of sets in topological spaces 5 % x has a countable base for its topology, or % y has a countable base for its topology, or ca each open set in x. On generalized topological spaces semantic scholar. The notion of gclosed sets is introduced in ideal topological spaces. It is then applied in reconstructing the important elements of.
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