Vol. 37, No. 2, 1971

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Co-absolutes of remainders of Stone-Čech compactifications

R. Grant Woods

Vol. 37 (1971), No. 2, 545–560

Let X be a completely regular Hausdorff space. Denote the “absolute” (also called the “projective cover”) of X by E(X), the Boolean algebra of regular closed subsets of X by R(X), and the Stone-Cech compactification of X by βX. In this paper it is proved that the canonical map k : E(βX)−≻ βX maps βE(X) E(X) irreducibly onto βX X if and only if the map A clρxAX is a Boolean algebra homomorphism from R(X) into R(βX X). This latter condition is shown to hold for a wide class of spaces X. These results are used to calculate absolutes and well-known co-absolutes of βXX under several different sets of hypotheses concerning the topology of X.

Mathematical Subject Classification 2000
Primary: 54D40
Received: 27 November 1970
Revised: 12 February 1971
Published: 1 May 1971
R. Grant Woods