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A novel class of bipolar soft separation axioms concerning crisp points

Baravan A. Asaad, Sagvan Y. Musa

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220189

The main objective of this study is to define a new class of bipolar soft (BS) separation axioms known as BS͠͠ Ti -space (i = 0, 1, 2, 3, 4). This type is defined in terms of ordinary points. We prove that BS͠͠ Ti -space implies BS͠͠ Ti-1-space for i = 1, 2; however, the opposite is incorrect, as demonstrated by an example. For i = 0, 1, 2, 3, 4, we investigate that every BS͠͠ Ti -space is soft͠ Ti -space; and we set up a conditio in which the reverse is true. Moreover, we point out that a BS subspace of a BS͠͠ Ti -space is a BS͠͠ Ti -space for i = 0, 1, 2, 3.