Abstract
The significance of the work is to introduce the new class of open sets which is said Ǥ-SP-open. many separation axioms by this notion was studied and the relationships between them like Ǥ-SP-𝒯0-space, Ǥ-SP-𝒯1-space, Ǥ-SP-𝒯2-space and Ǥ-SP-convergence sequence. moreover, by the sets understudy we introduce new convergence which is Ǥ-SP-convergence sequence . We will also study some functions such as open function them like Ǥ-SPO function, Ǥ∗-SPO function,Ǥ∗∗-SPO function ,continuous function G-SP-continuous function, strongly-Ǥ-SP-continuous function, Ǥ-SP-irresolute function. We will also study some definitions of axioms of separation and relationships between them.
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