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New Classes of Separation Axiom via Special Case of Local Function

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 لؤي عبد الهاني جبار السويدي
14/12/2016 10:15:23
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Shanin, 1943 [10] presented the notion of topological spaces, and Davis
[11] did that of topological spaces, studying certain characteristics of the weak
separation axioms as well as found some properties of topological spaces. The
idea of ideals in topological spaces has been studied by Kuratowski [4] and
Vaidyanathasamy [8]. An ideal I on a topological space (X,T) is a nonempty
collection of subsets of X which satisfies the following properties: (1) A ? I and B
? A implies B ? I. (2) A ? I and B ? I implies A?B ? I and called the (X,T,I) ideal
topological space. Ideal plays an important role in topics related to topological
domains as in separation axioms. Arenas, Dontchev and Puertas, 2008 [1]
unified some weak separation properties via topological ideals. Noiri and Keskin
2011 [12] introduced the notions of -sets in ideal topological spaces and
benefited from them in the definition of new types of weak separation axioms. In

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  • 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 .