International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 445-450
doi:10.1155/S0161171281000318
Semi separation axioms and hyperspaces
Department of Mathematics, Texas A&M University, College Station, Texas, USA
Received 21 April 1980; Revised 4 September 1980
Copyright © 1981 Charles Dorsett. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.