So, one can imagine that, how important the concept of closed sets is in the topological spaces. Conference series, volume 19, international conference on applied and computational mathematics 10 august 2018. 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. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided using regular sets. 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. Generalized alpha closed sets in neutrosophic topological. Generalized closed sets and open sets in topological spaces. By definition of a subset a of a topological space x is called generalized closed briefly, gclosed set if cla. On generalized closed sets in generalized topological spaces. Rajamani, studies on decompositions of generalized continuous maps in topological spaces, ph.
Second, we allow for the possibility that the whole space is not open. 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. 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. In this paper we introduce a new class of function. Generalized closed sets via neutrosophic topological spaces. If a subset a of x is a fuzzy soft generalized closed set in x and a. 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. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy. Neutrosophic generalized bclosed sets in neutrosophic topological spaces. Following the trend, we have introduced and investigated a kind of generalized closed sets in an ideal topological space. In 1970, levine initiated the study of socalled generalized closed sets.
Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college, devakottai. A note on modifications of rgclosed sets in topological spaces. Strong forms of stronger and weaker forms of continuous map have been in troduced and investigated by several mathematicians. Pdf on generalized closed sets in generalized topological. Every generalized b closed set in a topological space x is t generalized b closed. Let e be a generalized b closed set and e w, where w is t open in x. Pdf soft generalized closed sets in soft topological spaces. In 1970, levine9 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. R, pg student, nirmala college for women, coimbatore,tamil nadu. The notion of ideals in general topological spaces is treated in the classic text by kuratowski 4 and also in 10. Paper open access neutrosophic generalized bclosed sets in. Every topological space can be defined either with the help of axioms sets. Noiri gave a new type of generalized closed sets in topological space called gp closed sets.
It is obvious that in any topologicalspace x,everysgclosed subset of xis gs closed. Roy and erdal ekici, on, closed sets in generalized topological spaces, method of functional analysis and topology, 172 2011, 174179. Rajarubi abstract in this paper, we introduce a new class of sets called. On generalized closed sets and generalized preclosed sets. 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.
Generalized closed sets and open sets in topological. In 1970, levine7 introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. We also investigate several properties of such sets. Also, we introduce a new separation axiom of the topological spaces, and we prove that every space is a space. In this paper, the concept of generalized neutrosophic pre closed sets and generalized neutrosophic preopen sets are introduced. For example, one can define the topology on a set by using either the axioms for the closed sets or the. We also study relations and various properties between the other existing neutrosophic open and closed sets. Using generalized closed sets, dunham 1982 introduced the concept of generalized closure operator cl and obtained a class of topology, namely topology. 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.
On generalized closed sets in generalized topological. Using generalized closed sets, dunham8 introduced the concept of the closure operator cl and a new topology and studied some of their properties. New class of generalized closed sets in supra topological spaces. On a generalized closed sets in ideal topological spaces. Closed sets are fundamental objects in a topological space. Generalized closed sets in bitopological spaces pdf free.
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. The relationships among these new classes and existing classes of generalized closed. L, assistant professor, nirmala college for women, coimbatore, tamil nadu. Semi generalized bclosed sets in topological spaces 3. Some of their properties and characterizations are studied. Soft generalized closed sets in soft 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. This concept was found to be useful and many results in general topology were improved. Certain new classes of generalized closed sets and their.
On generalized closed sets and generalized preclosed sets in. Analogously, we begin this section by introducing the class of regular generalized. Paper open access neutrosophic generalized bclosed. Pdf on generalized closed sets and generalized preclosed. Saadati abstract we extend the notion of omega open set in ordinary topological spaces to generalized topological spaces. Benchalli and wali3 introduced the concept of rwclosed. Nagaveni, on weakly generalized continuous maps, weakly generalized closed maps and weakly generalized irresolute maps, far east. Generalized topological spaces in the sense of csaszar have two main features which distinguish them from typical topologies. Generalized closed sets in generalized topological. Semi generalized b closed sets in topological spaces 3. Neutrosophic generalized bclosed sets in neutrosophic. On generalized gp closed set in topological spaces.
New class of generalized closed sets in supra topological. Nour 5 found the characterizations of snormal spaces. In w 2 we shall define generalized closed written henceforth as gclosed sets and characterize them as. Abstract in this paper we introduce a new class of sets namely, gsclosed sets, properties of this set are investigated and we.
Benchalli and wali3 introduced the concept of rw closed. Noiri gave a new type of generalized closed sets in topological space called gp. Grill nano topological spaces with grill nano generalized. Ekici 3 introduced and studied bcontinuous functions in topological spaces.
Let a be a fuzzy soft generalized closed set such that a. Jeyaraman, 1 assistant professor, department of mathematics, rdm government arts college, sivagangai. Topology is a classical subject, as a generalization topological spaces many type of topological spaces introduced over the year. Semiconnectedness is characterized by using regular sets. Soft generalized closed sets in soft topological spaces article pdf available in journal of theoretical and applied information technology 371. Pdf on generalized closed sets in generalized topological spaces.
Chinthamani vasthirani, 2assosiate professor, department of mathematics, sree sevugan annamalai college. Veerakumar 15 defined gclosed sets in topological spaces and studied their properties. Then, the set fbgand fcgare t generalized b closed but not generalized closed. 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. In 20, the class of tgsspaces was introduced where a. We investigate various classes of generalized closed fuzzy sets in topological spaces, namely, closed fuzzy sets and closed fuzzy sets.
Fuzzy soft generalized closed sets in fuzzy soft topological. 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. Generalized closed sets in ideal topological spaces. Semi \cs\generalized closed sets in topological spaces. Generalized closed sets in generalized topological spaces 1m. Regular open sets have been introduced and investigated by stone 17. Generalized alpha closed sets in neutrosophic topological spaces d. On generalized semi b closed sets in topological spaces.
In 1970, levine studied the concept of generalized closed sets and a class of topological spaces called t 12 space. A subset s of a space xi is a topological space with an ide. Generalized closed sets via neutrosophic topological spaces a. Generalized closed sets in bitopological spaces journal of the egyptian mathematical society 2011 19, 142145 egyptian mathematical society journal of the egyptian mathematical society. 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.
First, these families of subsets are not closed under intersections. In this paper, the concept of generalized neutrosophic preclosed sets and generalized neutrosophic preopen sets are introduced. This type of set was investigated by ekici and caldas 2004 under the name of jopen sets. A subset a of a space x is called a delta generalized. Unification of generalized open sets on topological spaces. Pdf in this paper, we introduce several types of generalized closed sets in generalized topological spaces gtss. Roy, new generalized topologies on generalized topological spaces due to csa. A new class of generalized closed sets in topological spaces. The aim of this paper is to introduce a new class of sets called delta generalized. Soft regular generalized bclosed sets in soft topological spaces. 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. Generalized alpha closed sets in neutrosophic topological spaces. Hence, some points of the universe may be beyond any.
1186 460 1254 392 1112 717 1096 1498 63 1561 584 76 1521 1288 1062 215 620 566 287 1509 819 405 1155 868 1144 1155 1428 608 645 36