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Co-Absolutes with Homeomorphic Dense Subspaces

Published online by Cambridge University Press:  20 November 2018

Scott W. Williams
Scott W. Williams*
Affiliation:
SUNY/Buffalo, Buffalo, New York
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Recall that the absolute ∈(X) of a regular space X is the unique (up to a homeomorphism) extremally disconnected space whose image is X under a perfect irreducible map. X and Y are co-absolute whenever ∈(X) and ∈(Y) are homeomorphic. Completely regular spaces X and Y are weakly co-absolute whenever βX and βY are co-absolute. For a survey of this area we suggest [6] and [8].

In this paper we prove

THEOREM 1. Suppose, for i ∈ {0, 1};, X(i) is a compact connected linearly ordered space. Then X(0) and X(l) are co-absolute if, and only if, X(0) and X(l) have homeomorphic dense sets.

Making use of Theorem 1 and a result from [7] we give Theorem 2, a cardinal generalization of

COROLLARY 1. Suppose for each i ∈ {0, 1};, X(i) is a Čech-complete space with a Gδ-diagonal.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981 , pp. 857 - 861
Copyright
Copyright © Canadian Mathematical Society 1981

References

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