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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some Wallman compactifications determined by retracts


Author: H. L. Bentley
Journal: Proc. Amer. Math. Soc. 33 (1972), 587-593
MSC: Primary 54D35; Secondary 54C15
MathSciNet review: 0293588
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Abstract: Let Y be a Hausdorff compactification of a locally compact space X and let $ K = Y - X$ be the remainder. Suppose that K is a regular Wallman space (i.e. K has a base for closed sets which is a ring and which consists of sets each of which is the closure of its interior) and suppose that K is a neighborhood retract of Y. Under these assumptions, it is proved below that Y is a Wallman compactification of X.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293588-8
Keywords: Wallman compactification, normal base, locally compact space, retract
Article copyright: © Copyright 1972 American Mathematical Society