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Homeomorphic Sets of Remote Points

Published online by Cambridge University Press:  20 November 2018

R. Grant Woods
R. Grant Woods*
Affiliation:
The University of Manitoba, Winnipeg, Manitoba
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Let X be a completely regular Hausdorff space, and let βX denote the Stone-Čech compactification of X. A point p ∈ βX is called a remote point of βX if p does not belong to the βX-closure of any discrete subspace of X. Remote points were first defined and studied by Fine and Gillman, who proved that if the continuum hypothesis is assumed then the set of remote points of βR((βQ) is dense in βR – R(βQ – Q ) (R denotes the space of reals, Q the space of rationals). Assuming the continuum hypothesis, Plank has proved that if X is a locally compact, non-compact, separable metric space without isolated points, then βX has a set of remote points that is dense in βX – X. Robinson has extended this result by dropping the assumption that X is separable.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 3 , June 1971 , pp. 495 - 502
Copyright
Copyright © Canadian Mathematical Society 1971

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