Original Articles

SPACES WITH WALLMAN EQUIVALENT INTERMEDIATE SPACES

Published in: Quaestiones Mathematicae
Volume 16, issue 2, 1993, pages: 171–175
DOI: 10.1080/16073606.1993.9631728
Author(s): Cuebas LauraDepartment of Mathematics,, DarrellW. HajekDepartment of Mathematics,
Keywords: 54D30, 54D35

Abstract

If every infinite closed subset of the Wallman compactification, WX, of a space X must contain at least one element of X, then for any space Y intermediate between X and WX the Wallman compactification WY is homeomorphic to WX. This extends a property which characterizes normality inducing spaces. In the case where X is not normal, however, this is not a characterization, since there are nonnormal spaces for which all intermediate spaces are Wallman equivalent, but have infinite closed subsets contained in WX/X.

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