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. Pdf on generalized closed sets in generalized topological. Semi generalized b closed sets in topological spaces 3. We also study relations and various properties between the other existing neutrosophic open and closed sets. 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. Regular open sets have been introduced and investigated by stone 17. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college, devakottai. Unification of generalized open sets on topological spaces. On generalized closed sets in generalized topological. Let e be a generalized b closed set and e w, where w is t open in x. In this paper, the concept of generalized neutrosophic pre closed sets and generalized neutrosophic preopen sets are introduced. 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.
Rajamani, studies on decompositions of generalized continuous maps in topological spaces, ph. Roy and erdal ekici, on, closed sets in generalized topological spaces, method of functional analysis and topology, 172 2011, 174179. Abstract in this paper we introduce a new class of sets namely, gsclosed sets, properties of this set are investigated and we. A subset a of a space x is called a delta generalized. On generalized semi b closed sets in topological spaces. Benchalli and wali3 introduced the concept of rwclosed. Generalized closed sets and open sets in topological. 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. Pdf on generalized closed sets in generalized topological spaces. Paper open access neutrosophic generalized bclosed sets in. In this paper we introduce a new class of function. 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. Generalized alpha closed sets in neutrosophic topological spaces d. On generalized closed sets in generalized topological spaces.
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. A new class of generalized closed sets in topological spaces. Pdf on generalized closed sets and generalized preclosed. 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.
So, one can imagine that, how important the concept of closed sets is in the topological spaces. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. Semiconnectedness is characterized by using regular sets. Pdf soft generalized closed sets in soft topological spaces. In w 2 we shall define generalized closed written henceforth as gclosed sets and characterize them as. Following the trend, we have introduced and investigated a kind of generalized closed sets in an ideal topological space. Every topological space can be defined either with the help of axioms sets. Generalized closed sets in generalized topological spaces 1m. Rajarubi abstract in this paper, we introduce a new class of sets called. We investigate various classes of generalized closed fuzzy sets in topological spaces, namely, closed fuzzy sets and closed fuzzy sets. 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.
If a subset a of x is a fuzzy soft generalized closed set in x and a. The relationships among these new classes and existing classes of generalized closed. Ekici 3 introduced and studied bcontinuous functions in topological spaces. The aim of this paper is to introduce a new class of sets called delta generalized. Decompositions of regular open sets and regular closed sets are provided using regular sets. Soft generalized closed sets in soft topological spaces. We also investigate several properties of such sets. In 20, the class of tgsspaces was introduced where a.
A collection i px is called an ideal on x if it satis. On a generalized closed sets in ideal topological spaces. 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. Generalized alpha closed sets in neutrosophic topological. Topology is a classical subject, as a generalization topological spaces many type of topological spaces introduced over the year. Generalized closed sets in bitopological spaces pdf free. In this paper, the concept of generalized neutrosophic preclosed sets and generalized neutrosophic preopen sets are introduced. Soft generalized closed sets in soft topological spaces article pdf available in journal of theoretical and applied information technology 371.
Generalized closed sets and open sets in topological spaces. On generalized closed sets and generalized preclosed sets in. Semi \cs\generalized closed sets in topological spaces. Generalized closed sets in generalized topological.
Nagaveni, on weakly generalized continuous maps, weakly generalized closed maps and weakly generalized irresolute maps, far east. Generalized closed sets via neutrosophic topological spaces a. 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. Certain new classes of generalized closed sets and their. Every generalized b closed set in a topological space x is t generalized b closed. By definition of a subset a of a topological space x is called generalized closed briefly, gclosed set if cla. Analogously, we begin this section by introducing the class of regular generalized. Hence, some points of the universe may be beyond any. Nour 5 found the characterizations of snormal spaces.
In 1970, levine9 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. New class of generalized closed sets in supra topological. 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. 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. Properties of these sets are investigated for topological spaces and generalized topological spaces.
L, assistant professor, nirmala college for women, coimbatore, tamil nadu. Benchalli and wali3 introduced the concept of rw closed. Neutrosophic generalized bclosed sets in neutrosophic. The notion of ideals in general topological spaces is treated in the classic text by kuratowski 4 and also in 10. Andrijevic 1996 introduced a class of generalized open sets in a topological space called bopen sets. Second, we allow for the possibility that the whole space is not open. Veerakumar 15 defined gclosed sets in topological spaces and studied their properties. Noiri gave a new type of generalized closed sets in topological space called gp closed sets.
Jeyaraman, 1 assistant professor, department of mathematics, rdm government arts college, sivagangai. This type of set was investigated by ekici and caldas 2004 under the name of jopen sets. Pdf in this paper, we introduce several types of generalized closed sets in generalized topological spaces gtss. Neutrosophic generalized bclosed sets in neutrosophic topological spaces. On generalized closed sets and generalized preclosed sets in neutrosophic topological spaces wadei alomeri 1,, and saeid jafari 2, 1 department of mathematics, albalqa applied university, salt 19117, jordan 2 department of mathematics, college of vestsjaelland south, herrestraede 11, 4200 slagelse, denmark. Strong forms of stronger and weaker forms of continuous map have been in troduced and investigated by several mathematicians. A subset s of a space xi is a topological space with an ide. Generalized alpha closed sets in neutrosophic topological spaces.
Noiri gave a new type of generalized closed sets in topological space called gp. Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college. Generalized closed sets in bitopological spaces journal of the egyptian mathematical society 2011 19, 142145 egyptian mathematical society journal of the egyptian mathematical society. For example, one can define the topology on a set by using either the axioms for the closed sets or the. A note on modifications of rgclosed sets in topological spaces. New class of generalized closed sets in supra topological spaces. Paper open access neutrosophic generalized bclosed. Meena priyadarshini 1department of mathematics, kumaraguru college of technology, coimbatore, tamil nadu, india e mail. Generalized closed sets in ideal topological spaces. Roy, new generalized topologies on generalized topological spaces due to csa. Let a be a fuzzy soft generalized closed set such that a.
Generalized topological spaces in the sense of csaszar have two main features which distinguish them from typical topologies. Fuzzy soft generalized closed sets in fuzzy soft topological. R, pg student, nirmala college for women, coimbatore,tamil nadu. In 1970, levine initiated the study of socalled generalized closed sets. On generalized closed sets and generalized preclosed sets.
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 1970, levine studied the concept of generalized closed sets and a class of topological spaces called t 12 space. Soft regular generalized bclosed sets in soft topological spaces. Using generalized closed sets, dunham 1982 introduced the concept of generalized closure operator cl and obtained a class of topology, namely topology. Using generalized closed sets, dunham8 introduced the concept of the closure operator cl and a new topology and studied some of their properties. Grill nano topological spaces with grill nano generalized. Conference series, volume 19, international conference on applied and computational mathematics 10 august 2018. Saadati abstract we extend the notion of omega open set in ordinary topological spaces to generalized topological spaces. Some of their properties and characterizations are studied. Closed sets are fundamental objects in a topological space. First, these families of subsets are not closed under intersections. Generalized closed sets via neutrosophic topological spaces.
This concept was found to be useful and many results in general topology were improved. Chapter 3 semi generalized bclosed sets in topological spaces. It is obvious that in any topologicalspace x,everysgclosed subset of xis gs closed. In 1970, levine7 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces.