New Classes of Open Sets in Topological Spaces

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Beyda S. Abdullah, Sabih W. Askandar, Amir A. Mohammed

Abstract

In this paper, we have introduce a new open sets in topological spaces named ic-open sets. We present the relation of ic-open sets with other classes of open sets namely : semi-open, ,  and i  -open sets. Furthermore, we introduce the notion of ic-continuous map on topological spaces and we prove some properties and characterizations. Also, we study some separation axioms of this new class.   Finally, depending on ic-open sets we define a new class called icc-open set and we discuss the same results obtained by the first one, as each open (closed) set in a topological spaces of any kind  is icc-open (icc-closed) set

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