Vol. 105, No. 1, 1983

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Spaces without remote points

Eric Karel van Douwen and Jan van Mill

Vol. 105 (1983), No. 1, 69–75

All spaces considered are completely regular and X denotes βX X. The point x X is called a remote point of X if xClβXA for each nowhere dense subset A of X. If y Y , then the space Y is said to be extremally disconnected at y if yŪV whenever U and V are disjoint open sets. In this paper we construct two noncompact σ-compact spaces X, one locally compact and one nowhere locally compact, such that X has no remote points, and in fact such that βX is not extremally disconnected at any point.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54D40, 54G20
Received: 11 April 1978
Revised: 10 March 1982
Published: 1 March 1983
Eric Karel van Douwen
Jan van Mill