Omega open sets in generalized topological spaces samer al ghour, wafa zareer department of mathematics and statistics, jordan university of science and technology, irbid 22110, jordan. Following the trend, we have introduced and investigated a kind of generalized closed sets in an ideal topological space. Unification of generalized open sets on topological spaces. Neutrosophic generalized bclosed sets in neutrosophic topological spaces. In this paper, the concept of generalized neutrosophic preclosed sets and generalized neutrosophic preopen sets are introduced. Meena priyadarshini 1department of mathematics, kumaraguru college of technology, coimbatore, tamil nadu, india e mail. Using generalized closed sets, dunham8 introduced the concept of the closure operator cl and a new topology and studied some of their properties. We also investigate several properties of such sets. Generalized closed sets via neutrosophic topological spaces.
The aim of this paper is to introduce a new class of sets called delta generalized. Soft generalized closed sets in soft topological spaces. This applies, for example, to the definitions of interior, closure, and frontier in pseudometric spaces, so these definitions can also be carried over verbatim to a topological space. By definition of a subset a of a topological space x is called generalized closed briefly, gclosed set if cla. New class of generalized closed sets in supra topological spaces. On generalized gp closed set in topological spaces. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. Rajarubi abstract in this paper, we introduce a new class of sets called. Topology is a classical subject, as a generalization topological spaces many type of topological spaces introduced over the year.
Pdf soft generalized closed sets in soft topological spaces. The notion of ideals in general topological spaces is treated in the classic text by kuratowski 4 and also in 10. Generalized closed sets in generalized topological spaces 1m. For example, one can define the topology on a set by using either the axioms for the closed sets or the. L, assistant professor, nirmala college for women, coimbatore, tamil nadu. Chapter 3 semi generalized bclosed sets in topological spaces. On generalized closed sets and generalized preclosed sets. Nagaveni, on weakly generalized continuous maps, weakly generalized closed maps and weakly generalized irresolute maps, far east. Decompositions of regular open sets and regular closed sets are provided using regular sets. Generalized closed sets via neutrosophic topological spaces a. Paper open access neutrosophic generalized bclosed sets in. A subset s of a space xi is a topological space with an ide. 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.
A subset a of a space x is called a delta generalized. Request pdf on generalized gp closed set in topological spaces in this paper, the authors introduce a new class of sets called gp closed sets in topological spaces. Hence, some points of the universe may be beyond any. 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. Using generalized closed sets, dunham 1982 introduced the concept of generalized closure operator cl and obtained a class of topology, namely topology.
We also study relations and various properties between the other existing neutrosophic open and closed sets. On generalized closed sets in generalized topological spaces. In 20, the class of tgsspaces was introduced where a. Nandhini 2 abstract in this paper, we have introduced the notion of generalized closed sets in neutrosophic topological spaces and studied some of their basic properties. Analogously, we begin this section by introducing the class of regular generalized. In 1970, levine studied the concept of generalized closed sets and a class of topological spaces called t 12 space. In 1970, levine7 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. In 1970, levine9 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. Some of their properties and characterizations are studied. On generalized closed sets and generalized preclosed sets in. A collection i px is called an ideal on x if it satis.
The grill nano generalized closed sets is an expansion of nano generalized closed sets in grill nano topological spaces, which is the frame of reference measurement, inference and reasoning in many applications such as computer science and information systems. Benchalli and wali3 introduced the concept of rwclosed. Soft generalized closed sets in soft topological spaces article pdf available in journal of theoretical and applied information technology 371. Rajamani, studies on decompositions of generalized continuous maps in topological spaces, ph. Jeyaraman, 1 assistant professor, department of mathematics, rdm government arts college, sivagangai. Published 1 december 2018 published under licence by iop publishing ltd journal of physics. Then, the set fbgand fcgare t generalized b closed but not generalized closed. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy. Grill nano topological spaces with grill nano generalized. Semi generalized bclosed sets in topological spaces 3. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college, devakottai.
Semiconnectedness is characterized by using regular sets. Regular open sets have been introduced and investigated by stone 17. Noiri gave a new type of generalized closed sets in topological space called gp closed sets. In 1970, levine initiated the study of socalled generalized closed sets. Generalized alpha closed sets in neutrosophic topological spaces d. Fuzzy soft generalized closed sets in fuzzy soft topological. Pdf on generalized closed sets in generalized topological. Every topological space can be defined either with the help of axioms sets. In w 2 we shall define generalized closed written henceforth as gclosed sets and characterize them as. The relationships among these new classes and existing classes of generalized closed. A subset a of x is said to be ideal generalized closed set briefly ig closed set if a u whenever a u and u is open. Roy, new generalized topologies on generalized topological spaces due to csa.
Semi generalized b closed sets in topological spaces 3. Certain new classes of generalized closed sets and their. Generalized alpha closed sets in neutrosophic topological spaces. R, pg student, nirmala college for women, coimbatore,tamil nadu. This concept was found to be useful and many results in general topology were improved. Let a be a fuzzy soft generalized closed set such that a. Closed sets are fundamental objects in a topological space. Pdf on generalized closed sets in generalized topological spaces. Generalized closed sets in ideal topological spaces. A new class of generalized closed sets in topological spaces. Let e be a generalized b closed set and e w, where w is t open in x. 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. Abstract in this paper we introduce a new class of sets namely, gsclosed sets, properties of this set are investigated and we. Conference series, volume 19, international conference on applied and computational mathematics 10 august 2018.
Pdf on generalized closed sets and generalized preclosed. Pdf in this paper, we introduce several types of generalized closed sets in generalized topological spaces gtss. Saadati abstract we extend the notion of omega open set in ordinary topological spaces to generalized topological spaces. So, one can imagine that, how important the concept of closed sets is in the topological spaces. Strong forms of stronger and weaker forms of continuous map have been in troduced and investigated by several mathematicians. This type of set was investigated by ekici and caldas 2004 under the name of jopen sets.
Ekici 3 introduced and studied bcontinuous functions in topological spaces. Generalized closed sets in bitopological spaces pdf free. First, these families of subsets are not closed under intersections. If a subset a of x is a fuzzy soft generalized closed set in x and a.
Sarankumar 2 1 assistant professor, department of mathematics, cms college of science and commerce, coimbatore 2 research scholar, department of mathematics, cms college of science and commerce, coimbatore email. Second, we allow for the possibility that the whole space is not open. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college. It is obvious that in any topologicalspace x,everysgclosed subset of xis gs closed. Veerakumar 15 defined gclosed sets in topological spaces and studied their properties. New class of generalized closed sets in supra topological. In this paper, the concept of generalized neutrosophic pre closed sets and generalized neutrosophic preopen sets are introduced. Nour 5 found the characterizations of snormal spaces. Every generalized b closed set in a topological space x is t generalized b closed. A note on modifications of rgclosed sets in topological spaces. On generalized closed sets in generalized topological. On generalized semi b closed sets in topological spaces.
Neutrosophic generalized bclosed sets in neutrosophic. Generalized alpha closed sets in neutrosophic topological. Benchalli and wali3 introduced the concept of rw closed. Generalized closed sets and open sets in topological. Noiri gave a new type of generalized closed sets in topological space called gp. On a generalized closed sets in ideal topological spaces. Andrijevic 1996 introduced a class of generalized open sets in a topological space called bopen sets. Generalized closed sets and open sets in topological spaces. Paper open access neutrosophic generalized bclosed. In this paper we introduce a new class of function. Generalized closed sets in generalized topological. Generalized topological spaces in the sense of csaszar have two main features which distinguish them from typical topologies.