Some Weak Separation Axioms via (1, 2)Sβ-open sets in Bitopological spaces
Abstract
In topology, separation axioms establish the fundamental criteria for the degree of separation between different subsets. Weak separation axioms, an expansion of separation axioms offer a finer level of distinction between subsets. In 1963, Levine and Kelly initiated the notions of semi-open sets and bitopological spaces respectively. After that, many papers have been published to extend topological concepts to bitopological spaces. In this paper, we define a new class of semi-open sets namely (1, 2) Sβ - open sets by using (1, 2)semi - open sets in bitopological spaces. Also, we define and study (1, 2) Sβ -separation axioms in biopological spaces. We present some characterizations of weak separation axioms in bitopological spaces and the invariance properties by using (1, 2) Sβ - open sets. We compare some weak separation axioms among themselves and establish that the two pairs (1, 2) Sβ –RT space and (1, 2) Sβ –TYS are dependent on each other in general topology and independent on each other in bitopological spaces.
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