Rg closed sets in topological spaces pdf

We introduce the notions of sawirgclosed sets and weaklyrgiclosed by using the notion of regular open sets. Regular generalized closed sets in fuzzy ideal topological. The soft set theory was introduced by molodstov 8 in the year 1999. The notion of generalized closed sets in ideal topological spaces was studied by dontchev et. In this paper, the concept of fuzzy generalized regular star closed sets is introduced and studied. On contra rgcontinuous functions in topological spaces. Also we investigated the relationship between this type of space and other existing spaces. Pdf closed sets in topological spaces researchgate.

Then the collection of closed sets of xhas the following properties. In 1982, hdeib 5 introduced the notion of closed sets in topological spaces. 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. A subset a of x is said to be bgclosed if bcla u whenever a u and u is gopen in x. Maheswari and others published strongly g closed sets in topological spaces find, read and cite all the research you need on researchgate.

Soft regular generalized bclosed sets in soft topological. Thakur2 1department of applied mathematics, jabalpur engineering college jabalpur m. The main aim of this paper is to introduce some new related closed sets in the same space and study. On regular generalized open sets in topological space. In this section, grwopen sets in topological spaces and obtain some of their properties.

Closed sets, hausdor spaces, and closure of a set 9 8. The open and closed sets of a topological space examples 1 fold unfold. Norman levine 7 introduced generalized closed briefly gclosed sets in 1970. It is assumed that measure theory and metric spaces are already known to the reader. Its relationship with other existing sets are established. Since every rgclosed set is rgclosed, f is a rgclosed map. A new closure operator grwclosure in topological spaces. Hadi 3 1,2 department of mathematics, college of education for pure science almuthanna university, samawah, iraq 1email. Regular generalized star closed sets in bitopological spaces. On gnormal and gregular in ideal topological spaces 505 theorem 2. This new class of sets lies between the class of all wclosed sets and the class of all regular gclosed sets. Closed sets in nano topological spaces qays hatem imran 1, murtadha m. A note on modifications of rgclosed sets in topological spaces. J j college of arts and science, pudukkottai, tamilnadu.

Further, we study the concept of sawirgclosed sets and their relationships in ideal topological spaces by using these new notions. Next we show that this new class also properly contains the class of rgclosed sets, the class of gprclosed sets and the class of gspclosed sets. On soft gsrclosed sets in soft bitopological spaces. It has been proved that the class of pre generalized bclosed set lies between the class of bclosed sets and rgclosed sets. In this paper we introduce and study a new class of generalised closed sets called. 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. Union of two gclosed sets in x is a gclosed set in x. Regular generalized closed sets in fuzzy ideal topological spaces anita singh banafar1 and s. Every topological space can be defined either with the help of axioms sets. 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. On nano generalized alpha generalized closed sets in nano. Xis called open if it contains a neighborhood of each of its points. Palaniappan et al in 1993, introduced the notions of regular generalized in brief, rg closed sets, rgopen sets.

Sheik john et al 14 introduced gclosed sets in bitopological spaces. This new class falls strictly between the class of. The cartesian product m 1 m 2 is the set of all ordered pairs x 1. Palaniappan and rao17 introduced gspclosed sets, gprclosed sets and rgclosed sets. The converse of the above theorem need not be true as seen from the following example. The complement of an open set is said to be closed. Pdf regular gclosed sets in topological spaces researchgate. Levine in 1970, introduced the concept of generalized closed gclosed sets in topological space and a class of topological spaces called t 12 spaces. Paper 1, section ii 12e metric and topological spaces. In 1970, levine 11 introduced the notion of generalized closed briefly gclosed sets in topological spaces and showed that compactness, locally compactness. Some properties are proved and their relations with different fuzzy sets in fuzzy topological spaces are investigated. Also, grwneighbourhood in topological spaces by open sets.

International journal of mathematics trends and technology. Syed ali fathima department of mathematics sadakathullah appa college tirunelveli 627 011, india. On regular generalized open sets in topological space citeseerx. Suppose h is a subset of x such that f h is closed where h denotes the closure of h. Recently, many variations of gclosed sets are introduced and investigated. In this paper, we introduce a new class of sets called sbg closed sets in topological spaces. Introduction in 1970, levine 12 introduced the concept of generalized closed set in the topological spaces. In 1937, regular open sets were introduced and used to define the semiregularization space of a topological space. 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. One among them is g closed sets which were introduced by khalid y. Mariasingam post graduate and research department of mathematics, v.

The aim of this paper is to introduce the concept of g rconnected and g rcompactness in topological spaces. The notion of supra topological spaces was introduced by a. The aim of this paper is to introduce a new class of sets namely rg closed sets in topological spaces. Using generalized closed sets, dunham 1982 introduced. Later on jin han park3 studied the concept of regular generalized closed in fuzzy topological space. Vadivel et al 14 studied rg interior and rg closure sets in topological spaces. In this paper, we have introduced a new class of sets called bgclosed sets in topological spaces. Introduction to topological spaces and setvalued maps. Metricandtopologicalspaces university of cambridge. For the fuzzy topological spaces, g continuous fuzzy maps were introduced and studied by 6 and 5. Furthermore, we introduce and examine some properties of inormal space. In 1970, levine 7 introduced the notion of generalized closed gclosed sets in topological spaces. Also we discuss some of their properties and investigate the relations between the associated.

In this paper generalized regular closed sets is introduced in ideal topological spaces using semilocal function. The converse of the above theorem need not be true, as seen from the following example. The purpose of the present paper is to define a new class of closed sets called i, j. This class was obtained by generalizing closed sets via rg open sets which was introduced by n. 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. A generalized semipreclosed gspclosed set if spcla.