International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 445-450
doi:10.1155/S0161171281000318

Semi separation axioms and hyperspaces

Abstract

In this paper examples are given to show that s-regular and s-normal are independent; that s-normal, and s-regular are not semi topological properties; and that (S(X),E(X)) need not be semi-T1 even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T), (S(X),E(X)), (S(X0),E(X0)), and (S(XS0),E(XS0)) are homeomorphic, where (X0,Q(X0)) is the T0-identification space of (X,T) and (XS0,Q(XS0)) is the semi-T0-identification space of (X,T), and that if (X,T) is s-regular and R0, then (S(X),E(X)) is semi-T2.