Vol. 43, No. 2, 1972

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The disappearing closed set property

V. M. Klassen

Vol. 43 (1972), No. 2, 403–406
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 {Ui}i=1 such that Ui+1 Ui and i=1Ui = , and there is also a sequence {hi} of homeomorphisms on X onto X such that hi(C) Ui, 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
Authors
V. M. Klassen