Some Separation Axioms in Topological Spaces

Abstract

In this paper, we introduced the concepts of new separation axioms called $S{C}^{\ast }$-separation axioms and $H^{\ast }$-separation axioms by using $S{C}^{\ast }$ and $H^{\ast }$-open sets in topological spaces. The $S{C}^{\ast }$-separation axioms include $S{C}^{\ast }$-$C_0$, $S{C}^{\ast }$-$C_1$, weakly $S{C}^{\ast }$-$C_0$, and weakly $S{C}^{\ast }$-$C_1$ spaces, while the $H^{\ast }$-separation axioms include $H^{\ast }$-$T_{\frac{1}{2}}$, $H^{\ast }$-$T_b$, and $H^{\ast }$-$T_d$ spaces. Also, we obtained several properties of such spaces.