Compactifications of symmetrizable spaces

Burke, D. K.; Davis, S. W.

doi:10.1090/S0002-9939-1981-0601747-2

Compactifications of symmetrizable spaces
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by D. K. Burke and S. W. Davis PDF

Proc. Amer. Math. Soc. 81 (1981), 647-651 Request permission

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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