The purpose of the present work is to introduce and investigate a new class of sets in a topological spaces called S  – open sets. We use this set to define and study new concepts in topological spaces such as continuity, separation axioms, compactness  and dimension functions.

At the beginning of this work, we define the class of S β -open sets which contained in the class of semi-open sets . It is shown that the family of S β  -open sets form a supratopology on X. We prove that the family of S β – open sets and the family of semi-open sets are identical when ( X , ) is aT1-space or locally indiscrete and if a space X is hyperconnected then S  OX ) {.X }.


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