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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
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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Keywords: Symmetrizable, compactification, completely normal, perfectly normal
Article copyright: © Copyright 1981 American Mathematical Society

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