The Separation Properties of Binary Topological Spaces

Abstract

In the present study, we introduce some new separation axioms for binary topological spaces. This new idea gives the notion of generalized binary ( $T_0$ , $T_1$ , $T_2$ , $T_3$ , and $T_4$ spaces) and binary generalized semi ( $T_0$ , $T_1$ , $T_2$ , $T_3$ , and $T_4$ spaces) using generalized binary open sets and binary generalized semi open sets to investigate their properties. We also provide adequate examples to assist and understand abstract concepts. In the similar manner, we begin researching the b-sg- $T_0$ , b-sg- $T_1$ , b-sg- $T_2$ , b-sg- $T_3$ , and b-sg- $T_4$ spaces in binary topological spaces. The study on the axioms is done over binary- $T_0$ , binary- $T_1$ , binary- $T_2$ , binary- $T_3$ , and binary- $T_4$ spaces, motivated to do the analysis of the spaces gb(b-gs)- $T_0$ , gb(b-gs)- $T_1$ , gb(b-gs)- $T_2$ , gb(b-gs)- $T_3$ , and gb(b-gs)- $T_4$ as well.