Finally we show that certain results of several publications on the concepts of weakness and strength of fuzzy generalized closed. We also study relations and various properties between the other existing neutrosophic open and closed sets. The authors introduce new type of closed set named gp closed set in the topological. For the space x, the elements of are called open sets and the complement of open sets are called closed sets. In 1970, levine initiated the study of socalled generalized closed sets. On soft generalized closed sets in a soft topological. In this paper, we define and study about a new type of generalized closed set called, g. Certain new classes of generalized closed sets and their. In 1970, levine9 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces.
Metric spaces, topological spaces, and compactness a metric space is a set x. Levine 16 initiated the study of socalled generalized closed sets. We also investigate several properties of such sets. Generalized closed sets in generalized topological spaces 1m. A new class of locally closed sets and locally closed continuous functions in generalized topological spaces s. If ais a subset of x and b is a subset of y, then the topological structures on x and y provide a little. Semi generalized b closed sets in topological spaces 3. In this paper, the concept of fuzzy generalized regular star closed sets is introduced and studied. In 1970, levine 18 introduced the notion of gclosed sets in topological spaces as a generalization of closed sets. Also, some lower separation axioms weaker than t 1 are investigated. Parimelazhagan 7 defined closed sets of topological spaces.
Knebusch and their strictly continuous mappings begins. If u is a family of open sets in x, then s t u is open. In this paper, spaces always mean generalized topological spaces on which no separation axiom is assumed. Extending topological properties to fuzzy topological spaces by ruba mohammad abdulfattah adarbeh supervised by dr. The elements of in this paper the idea of locally closed sets in. Rajarubi abstract in this paper, we introduce a new class of sets called. Firstly the notion of igclosed set is given by dontchev et al. Recently, many variations of gclosed sets are introduced and investigated. Andrijevic 1996 introduced a class of generalized open sets in a topological space called bopen sets. We investigate various classes of generalized closed fuzzy sets in topological spaces, namely, closed fuzzy sets and closed fuzzy sets. It is then applied in reconstructing the important elements of.
A study on some generalizations of delta closed sets in. On generalized closed sets in generalized topological. For any set x, we have a boolean algebra px of subsets of x, so this algebra of sets may be treated as. Suguna selvarani department of mathematics, svs college of engineering, coimbatore, tamilnadu abstract. Later on jin han park3 studied the concept of regular generalized closed in fuzzy topological space. Abstract in this paper we have introduced a new class of sets called c o l. 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. Also, he obtained and studied the notions of semiopen sets, preopen sets. Dontchev and maki have introduced the concept of generalized closed. In this paper, we introduce and study the new concept of binary generalized topological spaces.
Almost contra pre generalized b continuous functions in topological spaces theorem 3. Using generalized closed sets, dunham8 introduced the concept of the closure operator cl and a new topology and studied some of their properties. Extending topological properties to fuzzy topological spaces. Levine introduced generalized closed sets in topological spaces. Chapter 3 semi generalized bclosed sets in topological spaces. In the year 2014, the present authors introduced and studied the concept of gclosed sets in topological spaces. In 1970, levine 10 introduced the notion of generalized closed gclosed sets in topological spaces. In this paper, the concept of generalized neutrosophic pre closed sets and generalized neutrosophic preopen sets are introduced. The notion of ideals in general topological spaces is treated in the classic text by kuratowski 4 and also in 10. On regular generalized open sets in topological space. Generalized topology of gtspace has the structure of frame and is closed under arbitrary unions and. Also, we introduce some characterizations and properties for these concepts.
Supra generalized closed soft sets with respect to an soft. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college. Following the trend, we have introduced and investigated a kind of generalized closed sets in an ideal topological space. Some new regular generalized closed sets in ideal topological. The family of all gopen subsets of xand the family of all g closed subsets of xare denoted by gox and gcx, respectively. Nagaveni assistant pro fessor coimbatore institute of technology, coimbatore, india. A subset a of x is said to be bg closed if bcla u whenever a u and u is gopen in x. Introduction to generalized topological spaces irina zvina abstract we introduce the notion of generalized topological space gtspace.
Unification of generalized open sets on topological spaces. Indeed ideals are very important tools in general topology. In this paper, we have introduced a new class of sets called bg closed sets in topological spaces. Closed sets in topological spaces pauline mary helen m, associate professor,nirmala college, coimbatore. Semi generalized bclosed sets in topological spaces 3. We will consider the question of when some classes of generalized closed sets coincide. Jeyaraman, 1 assistant professor, department of mathematics, rdm government arts college, sivagangai. In this paper another generalization of igclosed sets namely g i eclosed set is defined using semipre local function.
On generalized closed sets in generalized topological spaces. The aim of this paper is to continue the study of gpclosed sets thereby contributing new innovations and concepts in the field of topology through analytical as well as research works. On a type of generalized open sets roy applied general. Soft generalized closed sets with respect to an ideal in. Ever since general topologists extend the study of generalized closed sets on the basis of generalized semiopen sets, semi generalized open sets, generalized open sets, semiopen sets, preopen sets and d open sets, semipreopen sets. The notion of gpclosed sets and its different characterizations. Some properties are proved and their relations with different fuzzy sets in fuzzy topological spaces are investigated. On generalized topological spaces semantic scholar. In this paper, we introduce and study the concept of soft generalized closed sets with respect to a soft ideal, which is the extension of the concept of soft generalized closed sets. A new class of locally closed sets and locally closed. The family of small subsets of a gtspace forms an ideal that is. Using generalized closed sets, dunham 1982 introduced the concept of generalized closure operator cl and. Soft sets, soft topological space,open soft, closed soft, supra soft topological space, supra open soft, supra closed soft.
Meena priyadarshini 1department of mathematics, kumaraguru college of technology, coimbatore, tamil nadu, india e mail. On a type of generalized open sets in this paper, a new class of sets called. On generalized closed sets and generalized preclosed sets. In 1997, fuzzy generalized closed set briefly was introduced by g.
Some new regular generalized closed sets in ideal topological spaces umit karab. Pdf closed sets in topological spaces researchgate. For a x, we denote by a the intersection of all closed sets. Informally, 3 and 4 say, respectively, that cis closed under. On generalized gp closed set in topological spaces. The aim of this work is to introduce operations on fuzzy topological spaces and to use them to study fuzzy generalized closed sets and fuzzy generalized open sets. A collection i px is called an ideal on x if it satis. In this paper we introduce and characterize some new generalized locally closed sets known as. We will provide characterizations of extremally disconnected spaces and sgsubmaximal spaces by using various kinds of generalized closed sets. Pdf on generalized closed sets and generalized pre.
Closed sets in topological spaces semantic scholar. Veera kumar 12 introduced gclosed sets in topological spaces. X, we denote by s the closure of s the smallest closed subset of xcontaining s, i. On some locally closed sets and spaces in ideal topological. A subset a of x is said to be bgclosed if bcla u whenever a u and u is gopen in x. 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. Cs asz ar founded the theory of generalized topological spaces and. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. If k is a family of closed subsets of x, then k is closed. 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.
In this paper another generalization of igclosed sets namely g i. The purpose of this paper is to define a new class of sets called closed sets and also study some basic properties and characterizations. December 2016 on generalized closed sets in generalized topological spaces b. Khan and noiri 3 have introduced semilocal functions in ideal topological spaces. Chauhan2 1 department of mathematics, atmaram sanatan dharma college, university of delhi. 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 soft generalized closed sets in soft topological spaces.
So, one can imagine that, how important the concept of closed sets is in the topological spaces. The investigation on generalization of closed set has lead to significant contribution to the theory of separation axiom, generalization of continuity and irresolute functions. Closed sets in ideal topological spaces iosr journals. Also glocally closed continuous briefly glccontinuous functions and its irresolute. The concept of soft generalized closed sets in soft topological spaces was introduced by kannan 1. The study of generalized closed sets was initiated by levine 1970 in order to extend some important. Closed sets are fundamental objects in a topological space. Supra generalized closed soft sets with respect to an. It is observed that a large number of papers are devoted to the study of generalized open sets like open. Extension research of generalized closedness was done in recent years as the notion of generalized semiopen sets, semi generalized open sets, generalized open sets, semiopen sets, preopen sets and d open sets, semi preopen sets were investigated. Between closed sets and closed sets in topological spaces. Almost contra pre generalized b continuous functions in. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy.
The study of generalized closed sets in a topological space was initiated by levine in 7 and the concept of t12 spaces was introduced. On generalized topological spaces arturpiekosz abstract in this paper a systematic study of the category gtsof generalized topological spaces in the sense of h. Here is another useful property of compact metric spaces, which will eventually be generalized even further, in e. Separation spaces in generalized topology 67 a generalized topology is said to be strong 2 if x. Every topological space can be defined either with the help of axioms sets. Ais a family of sets in cindexed by some index set a,then a o c. 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. In this paper, we have introduced a new class of sets called bgclosed sets in topological spaces. For x2x, the family of all gopen subsets containing xand the family of all g closed. On generalized closed sets in topological spaces dr.
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