New classes of separation axiom via special case of local function

Abstract

In this paper, are investigated some new weak separation axioms connected with "Gem set". Besides are both introduced and studied some of their properties and the relation between them and other weak separation axioms is highlighted .

operator Proximity in i-Topological Space

“…Then this idea was presented and developed by the Russian scientist Efremovic [3] and presented by the name of infinitesmma1 spaces in a series of research, and then he generalized the concept of proximity spaces by using the meaning of proximity neighborhood After that, the proximity spaces witnessed a clear development through the many and varied researches included the concept like [4,15,19,20]. As for the concept of ideal and ideal topology, it was introduced by the scientist K. Kuratowski in 1933[2], and this topic has witnessed many different researches that dealt with various aspects of this topic such as [23,13,12]. The i-topology, it is another form of topological spaces defined by the use of the family T with the ideal I , as it was defined by Irina Zvina in 2006 [6].…”

New Concepts of Dense set in i-Topological space and Proximity Space

“…In 1909 Riecs [10] introduce the concept of proximity relation then this concept was developed by Efremovic in 1952 [21] as this concept has been used on a large scale to produce a huge amount of different research in various disciplines like [3,4,8,11] After Kartowski's definition [9] of ideal in 1933 and his definition of ideal topological spaces which includes two structures, the ideal I and topological space (X,T) , these concepts played a major role in the development of researches for a large number of researchers in various studies like [2,5,6] . A new topology for X has been constructed from the family T and the ideal I defined by Irina [6]and its called the i-topological space which includes checked the following condition (1) , (2)for any there exist such that (3)for each there exist such that Where defined by A B iff Our work here includes studying the influences that can appear on some topological characteristics in i-topolgical space through their application using the proximity theory, and among these characteristics are: adherent point, density, resolvability as it was relying on some concepts that were presented in previous research [20] Let (X,T1, ) and (X,T2, ) are -Topological spaces then we say that T1 ideal link to T2 if for each U is proper subset of X in T1 there exist a proper subset of X ,V in T2 Such that If T1 is ideal link to T2 we denoted that by T1 Ϫ T2 Example (5-2) :…”

On Soft Turning Points

“…In 2015 Aysequl and Goknur (10) introduced I_ regular, I_ normal and found a squire relations between them. The properties for instance, separation axioms and compactness to more details (11,12). Moreover, Kanal el at.…”