The disappearing closed set property

V. M. Klassen

Vol. 43 (1972), No. 2, 403–406

DOI: 10.2140/pjm.1972.43.403

Abstract

A topological space X is said to have the disappearing closed set (DCS) property or to be a DCS space, if for every proper closed subset C there is a family of open sets {U_i}_i=1^∞ such that U_i+1 ⊆ U_i and ⋂ _i=1^∞U_i = ∅, and there is also a sequence {h_i} of homeomorphisms on X onto X such that h_i(C) ⊆ U_i, for all i. Properties of DCS spaces are studied as are connections between this and other related definitions.

Mathematical Subject Classification 2000

Primary: 54D99

Milestones

Received: 11 August 1971

Published: 1 November 1972