Vol. 85, No. 1, 1979

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On spaces whose Stone-Čech compactification is Oz

Toshiji Terada

Vol. 85 (1979), No. 1, 231–237
Abstract

A Tychonoff space X is called Oz if every open subset is z-embedded in X. In this paper we characterize a class of spaces whose Stone-Čech compactifications are Oz. Especially it is shown that for a realcompact Oz-space of countable type, βX is Oz if and only if X is expressed as the union of an extremally disconnected subset and a compact subset.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54C45
Milestones
Received: 14 March 1978
Revised: 8 January 1979
Published: 1 November 1979
Authors
Toshiji Terada