Another Class of Cyclicly Extensible and Reducible Properties

Abstract

AbstractA space S has property P-1 if S is nonempty. For n > — 1, S has property Pn if it is locally connected, has property Pn-1 and if whenever it is written as a union, S = A ∪ B where each of A and B is closed and has property Pn-1, then A ∩ B also has property Pn-1. The purpose of this paper is to establish that for locally compact spaces, each of the properties Pn is both cyclicly extensible and reducible.