Rg closed sets in topological spaces pdf

The notion of generalized closed sets in ideal topological spaces was studied by dontchev et. Levine in 1970, introduced the concept of generalized closed gclosed sets in topological space and a class of topological spaces called t 12 spaces. 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. On soft gsrclosed sets in soft bitopological spaces. Regular generalized star closed sets in bitopological spaces. A generalized semipreclosed gspclosed set if spcla. On contra rgcontinuous functions in topological spaces. Hadi 3 1,2 department of mathematics, college of education for pure science almuthanna university, samawah, iraq 1email. The main aim of this paper is to introduce some new related closed sets in the same space and study. The notion of pre generalized bclosed sets and its di. The cartesian product m 1 m 2 is the set of all ordered pairs x 1. A subset a of a topological space is said to be locally closed 4 if it is the intersection of an open set and a closed set.

It is assumed that measure theory and metric spaces are already known to the reader. Sheik john et al 14 introduced gclosed sets in bitopological spaces. On regular generalized open sets in topological space citeseerx. On regular generalized open sets in topological space. Paper 1, section ii 12e metric and topological spaces. In 1970, levine 7 introduced the notion of generalized closed gclosed sets in topological spaces. The complement of an open set is said to be closed. Regular generalized closed sets in fuzzy ideal topological spaces anita singh banafar1 and s. In this paper, a generalized class of tau called weakly i rg open sets in ideal topological spaces is introduced and the notion of weakly i rg closed sets in ideal topological spaces is studied. The converse of the above theorem need not be true, as seen from the following example. Metricandtopologicalspaces university of cambridge. One among them is g closed sets which were introduced by khalid y. In this paper, we have introduced a new class of sets called bgclosed sets in topological spaces. Suppose h is a subset of x such that f h is closed where h denotes the closure of h.

The purpose of the present paper is to define a new class of closed sets called i, j. International journal of mathematics trends and technology. Palaniappan and rao17 introduced gspclosed sets, gprclosed sets and rgclosed sets. The aim of this paper is to introduce a new class of sets namely rg closed sets in topological spaces. The soft set theory was introduced by molodstov 8 in the year 1999. 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. Vadivel et al 14 studied rg interior and rg closure sets in topological spaces. Pdf closed sets in topological spaces researchgate. Norman levine 7 introduced generalized closed briefly gclosed sets in 1970. Pdf regular gclosed sets in topological spaces researchgate. A note on modifications of rgclosed sets in topological spaces. If f is closed and a is a gclosed set such that a\f. Syed ali fathima department of mathematics sadakathullah appa college tirunelveli 627 011, india. Let a be a g closed set in x such that a u, where u is gopen.

Also we discuss some of their properties and investigate the relations between the associated. Introduction to topological spaces and setvalued maps. Using generalized closed sets, dunham 1982 introduced. This class was obtained by generalizing closed sets via rg open sets which was introduced by n. Every topological space can be defined either with the help of axioms sets. For the fuzzy topological spaces, g continuous fuzzy maps were introduced and studied by 6 and 5. Its relationship with other existing sets are established. Soft regular generalized bclosed sets in soft topological. It has been proved that the class of pre generalized bclosed set lies between the class of bclosed sets and rgclosed sets. A new closure operator grwclosure in topological spaces. Furthermore, we introduce and examine some properties of inormal space. The notion of supra topological spaces was introduced by a. Further closed sets like i rg,i rw were further developed by navaneethakrishnan 10 and a.

Since every rgclosed set is rgclosed, f is a rgclosed map. The aim of this paper is to introduce the concept of g rconnected and g rcompactness in topological spaces. On nano generalized alpha generalized closed sets in nano. Some properties are proved and their relations with different fuzzy sets in fuzzy topological spaces are investigated. A subset a of x is said to be bgclosed if bcla u whenever a u and u is gopen in x. Closed sets in topological spaces article pdf available in international journal of mathematical analysis 839. Closed sets in nano topological spaces qays hatem imran 1, murtadha m. We introduce the notions of sawirgclosed sets and weaklyrgiclosed by using the notion of regular open sets.

Mariasingam post graduate and research department of mathematics, v. Further, we study the concept of sawirgclosed sets and their relationships in ideal topological spaces by using these new notions. The aim of this paper is to introduce a new class of sets namely rg closed sets in topological spaces and study some basic properties. In this paper, we introduce a new class of sets called sbg closed sets in topological spaces.

Maheswari and others published strongly g closed sets in topological spaces find, read and cite all the research you need on researchgate. Closed sets, hausdor spaces, and closure of a set 9 8. In this paper, the concept of fuzzy generalized regular star closed sets is introduced and studied. In this section, grwopen sets in topological spaces and obtain some of their properties. Palaniappan et al in 1993, introduced the notions of regular generalized in brief, rg closed sets, rgopen sets. Union of two gclosed sets in x is a gclosed set in x. Also, grwneighbourhood in topological spaces by open sets. In 1937, regular open sets were introduced and used to define the semiregularization space of a topological space. This new class of sets lies between the class of all wclosed sets and the class of all regular gclosed sets. Also we investigated the relationship between this type of space and other existing spaces. The open and closed sets of a topological space examples 1.

The converse of the above theorem need not be true as seen from the following example. In this paper generalized regular closed sets is introduced in ideal topological spaces using semilocal function. Xis called open if it contains a neighborhood of each of its points. Recently, many variations of gclosed sets are introduced and investigated. In this paper we introduce and study a new class of generalised closed sets called. Thakur2 1department of applied mathematics, jabalpur engineering college jabalpur m. In 1970, levine 11 introduced the notion of generalized closed briefly gclosed sets in topological spaces and showed that compactness, locally compactness. Then the collection of closed sets of xhas the following properties. J j college of arts and science, pudukkottai, tamilnadu. Regular generalized closed sets in fuzzy ideal topological. Later on jin han park3 studied the concept of regular generalized closed in fuzzy topological space. In 1982, hdeib 5 introduced the notion of closed sets in topological spaces. This new class falls strictly between the class of. On gnormal and gregular in ideal topological spaces 505 theorem 2.