Results about the Alexandroff duplicate space

Abstract

In this paper, we present some new results about the Alexandroff Duplicate Space. We prove that if a space X has the property P, then its Alexandroff Duplicate space A(X) may not have P, where P is one of the following properties: extremally disconnected, weakly extremally disconnected, quasi-normal, pseudocompact. We prove that if X is α-normal, epinormal, or has property wD, then so is A(X). We prove almost normality is preserved by A(X) under special conditions.