Also glocally closed continuous briefly glccontinuous functions and its irresolute functions are. Separation spaces in generalized topology 67 a generalized topology is said to be strong 2 if x. Using generalized closed sets, dunham 1982 introduced the concept of. A subset a of a generalized topological space we recall some notion defined in 1, 2. 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. Pdf in this paper, we introduce several types of generalized closed sets in generalized topological spaces gtss. Introduction zadeh 1 introduced the notion of fuzzy sets. Also, roy and samanta strengthen the definition of the soft topological spaces presented in and they used the base and the subbase to characterize its properties. Full text of on some locally closed sets and spaces in. Ijmms semiprecontinuous functions and properties of generalized semipreclosed sets in topological spaces andrijevi. Also we study some of its basic properties and investigate the relations between the associated topology.
Decompositions of regular open sets and regular closed sets are provided using regular sets. Full text of on some locally closed sets and spaces in ideal topological spaces see other formats international open 9 access journal of modern engineering research ijmer on some locally closed sets and spaces in ideal topological spaces 12 3 m. In the year 2014, the present authors introduced and studied the concept of gclosed sets in topological spaces. 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. The family of small subsets of a gtspace forms an ideal that is. The investigation on generalization of closed set has lead to significant contribution to the theory of separation axiom, generalization of continuity and irresolute functions. Following the trend, we have introduced and investigated a kind of generalized closed sets in an ideal topological space. Recently, some results on intuitionistic fuzzy generalized minimal closed sets were introduced by bhattacharya 8 in 2010.
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. On generalized closed sets in generalized topological spaces. Andrijevic 1996 introduced a class of generalized open sets in a topological space called bopen sets. A collection i px is called an ideal on x if it satis. On generalized topological spaces artur piekosz abstract arxiv. December 2016 on generalized closed sets in generalized topological spaces b. I found this article on tilde mu open sets in generalized topological spaces and from the article these sets are defined as follows. Generalized star semiclosed sets in topological spaces. Theory of generalized sets in generalized topological spaces. In this paper the structure of these sets and classes of sets are investigated, and some applications are given. Generalized closed sets and open sets in topological spaces. On regular generalized open sets in topological space. On generalized closed sets article pdf available in topology and its applications 1231.
Abstract in this paper we have introduced a new class of sets called c o l. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. On generalized closed sets in generalized topological. We investigate various classes of generalized closed fuzzy sets in topological spaces, namely, closed fuzzy sets and closed fuzzy sets. A subset a of a space x is called bcopen if for each, there exists a closed set f such that. Ais a family of sets in cindexed by some index set a,then a o c. In this paper we introduce and characterize some new generalized locally closed sets known as.
Knebusch and their strictly continuous mappings begins. Semiconnectedness is characterized by using regular sets. Meena priyadarshini 1department of mathematics, kumaraguru college of technology, coimbatore, tamil nadu, india e mail. A new class of generalized closed sets in topological spaces. Chauhan2 1 department of mathematics, atmaram sanatan dharma college, university of delhi. Further, gspcontinuous, and gsp irresolute mappings are also introduced and investigated. In 1970, levine6 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. In this paper, we introduce the notion of intuitionistic fuzzy 8 generalized closed. Nagaveni assistant pro fessor coimbatore institute of technology, coimbatore, india.
Properties of these sets are investigated for topological spaces and generalized topological spaces. In this paper, the concept of fuzzy generalized regular star closed sets is introduced and studied. Certain new classes of generalized closed sets and their. Generalized closed sets in bitopological spaces pdf. Generalized double fuzzy closed sets in bitopological spaces different families of sets in bitopological spaces generalized fuzzy bclosed and generalized. Vigneshwaran abstract in this paper we introduce i.
Pdf on generalized closed sets and generalized pre. This type of set was investigated by ekici and caldas 2004 under the name of jopen sets. S, is the intersection of generalized closed sets including s. Closed sets are fundamental objects in a topological space. A subset a of a space x is called a delta generalized. Closed sets in topological spaces pauline mary helen m, associate professor,nirmala college, coimbatore. A subset a of a topological space x is called generalized closed set briefly gclosed if cl a g whenever a g and g is.
Veera kumar 12 introduced gclosed sets in topological spaces. Cs asz ar founded the theory of generalized topological spaces and. In this section, we introduce a new class of bopen sets called bcopen sets in topological spaces. These are closed sets so there complement must be open i stack exchange network. Informally, 3 and 4 say, respectively, that cis closed under.
In this paper another generalization of igclosed sets namely g i eclosed set is defined using semipre local function. On generalized topological spaces pdf free download. In this paper, the concept of generalized neutrosophic pre closed sets and generalized neutrosophic preopen sets are introduced. Levine4 introduced the notion of generalized closed brie y gclosed sets. Using generalized closed sets, dunham8 introduced the concept of the closure operator cl and a new topology and studied some of their properties. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a pdf plugin installed and enabled in your browser. The purpose of this paper to introduce a new class of locally closed sets called glocally closed sets briefly glcsets and study some of their properties. For a x, we denote by a the intersection of all closed sets. An ideal on a set x is a nonempty collection of subsets of x with heredity property which is also closed under finite unions. Several specific types of generalized sets of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. The open sets in a topological space are those sets a for which a0. Semiprecontinuous functions and properties of generalized.
On soft generalized closed sets in a soft topological. As an application, we introduce two news paces namely, tgspspace, gtgspspace. Lo 12 jun 2009 in this paper a systematic study of the category gts of generalized topological spaces in the sense of h. Semi generalized bclosed sets in topological spaces 3. Pdf closed sets in topological spaces researchgate. The khalimsky topology plays a significant role in the digital image processing. The elements of in this paper the idea of locally closed sets in. Recently, some results on intuitionistic fuzzy generalized minimal closed sets were introduced by bhattacharya in 2010. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy. The family of all bcopen subsets of a topological space is denoted by or briefly. A note on modifications of rgclosed sets in topological spaces. We also study relations and various properties between the other existing neutrosophic open and closed sets. Some properties are proved and their relations with different fuzzy sets in fuzzy topological spaces are investigated.
We study some new classes of generalized closed sets. In this paper, we introduce the notion of intuitionistic fuzzy. The concept of generalized closed sets in bitopological spaces was introduced by sundaram. 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. Pdf in this paper we study generalized closed sets in the sense of n. Rajarubi abstract in this paper, we introduce a new class of sets called. Pdf on generalized closed sets in generalized topological spaces. In this section, a new class of set called generalized closed set is introduced and some of its properties are studied.
Every topological space can be defined either with the help of axioms sets. Levine 16 initiated the study of socalled generalized closed sets. The notion of ideals in general topological spaces is treated in the classic text by kuratowski 4 and also in 10. Pious missier 1 department of mathematics, kamaraj college, thoothukudi, tamilnadu, india. In 1970, levine initiated the study of socalled generalized closed sets. In this paper, we introduce and study the concept of generalized closed sets with respect to an ideal in an ideal bitopological space. So, one can imagine that, how important the concept of closed sets is in the topological spaces. Using generalized closed sets, dunham5 introduced the concept of the closure operator c1 and a new topology and studied some of their properties. A new class of locally closed sets and locally closed continuous functions in generalized topological spaces s. Dontchev and maki have introduced the concept of generalized closed. In 1970, levine9 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. Later on jin han park3 studied the concept of regular generalized closed in fuzzy topological space.
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