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Proceedings of the American Mathematical Society

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

 
 

 

Compactifications of symmetrizable spaces


Authors: D. K. Burke and S. W. Davis
Journal: Proc. Amer. Math. Soc. 81 (1981), 647-651
MSC: Primary 54D35; Secondary 54E25
DOI: https://doi.org/10.1090/S0002-9939-1981-0601747-2
MathSciNet review: 601747
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Abstract: In response to questions of Arhangel'skiĭ, we present examples of (1) $ ({\text{MA}} + \neg {\text{CH}})$ a symmetrizable space which is not metrizable but has a completely normal compactification and (2) $ ({\text{CH}})$ a symmetrizable space which is not metrizable but has a perfectly normal compactification. In the construction of (2), a technique is developed which can be used to obtain first countable compactifications of many interesting examples.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0601747-2
Keywords: Symmetrizable, compactification, completely normal, perfectly normal
Article copyright: © Copyright 1981 American Mathematical Society

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