1981•Proceedings of the American Mathematical SocietyRequires access
Compactifications of symmetrizable spaces
Dennis K. Burke, S. W. Davis
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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.