On a theorem of Arhangelskiĭ

Author:
H. H. Hung

Journal:
Proc. Amer. Math. Soc. **82** (1981), 629-633

MSC:
Primary 54D18; Secondary 54E35

DOI:
https://doi.org/10.1090/S0002-9939-1981-0614891-0

MathSciNet review:
614891

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Abstract | References | Similar Articles | Additional Information

Abstract: We define a class of spaces which is more extensive than the class of BCO spaces and which counts among its members some that are not even first countable, and show that this more extensive class of spaces nevertheless intersects the class of paracompact Hausdorff spaces at precisely the class of metrizable spaces as does the class of BCO spaces, thus extending a theorem of Arhangel'skiĭ. We further show that this extension of Arhangel'skiĭ's result has gone the farthest in the sense that any class of spaces that meets the paracompact spaces at precisely the metrizable spaces must, among the Hausdorff spaces, be smaller than the class we have defined.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0614891-0

Keywords:
Paracompactness,
BCO,
metrizability,
largest class to meet the paracompact at the metrizable

Article copyright:
© Copyright 1981
American Mathematical Society