Hypersoft Separation Axioms

Abstract

 In this manuscript, we continue to study hypersoft topological space (briefly, HSTS) by presenting hypersoft (HS) separation axioms, called HS $T_i$-space for $i = 0, 1, 2, 3, 4$. The notions HS regular spaces and HS normal spaces are both thoroughly explained. We look into the connections between them and present numerous examples to help clarify the interconnections between different types of these spaces. We point out that HS $T_i$-axioms imply HS $T_{i-1}$ for $i = 1, 2, 3$, and with the help of an example we show that HS $T_4$-space need not be HS $T_3$-space. We also elucidate that the property of a HS space being HS $T_i$-space $(i = 0, 1, 2, 3)$ is HS hereditary.