Convergent free sequences in compact spaces

Authors:
I. Juhász and Z. Szentmiklóssy

Journal:
Proc. Amer. Math. Soc. **116** (1992), 1153-1160

MSC:
Primary 54D35

DOI:
https://doi.org/10.1090/S0002-9939-1992-1137223-8

MathSciNet review:
1137223

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Abstract: We prove that if is an uncountable regular cardinal and a compact space contains a free sequence of length , then also contains such a sequence that is convergent. This implies that under every nonfirst countable compact space contains a convergent -sequence and every compact space with a small diagonal is metrizable, thus answering old questions raised by the first author and M. Hušek, respectively.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1137223-8

Article copyright:
© Copyright 1992
American Mathematical Society