A remark on irreducible spaces

Author:
J. C. Smith

Journal:
Proc. Amer. Math. Soc. **57** (1976), 133-139

MSC:
Primary 54D20

DOI:
https://doi.org/10.1090/S0002-9939-1976-0405353-2

MathSciNet review:
0405353

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Abstract: A topological space is called irreducible if every open cover of has an open refinement which covers minimally. In this paper we show that weak -refinable spaces are irreducible. A modification of the proof of this result then yields that -compact, weak -refinable spaces are Lindelöf. It then follows that perfect, -compact weak -refinable spaces are irreducible. A number of known results follow as corollaries.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0405353-2

Keywords:
Metacompact,
-refinable,
weak -refinable,
-refinable,
weak -refinable,
-compact,
compact,
countably compact,
Lindelöf,
minimal cover,
irreducible,
maximal distinguished set,
perfect

Article copyright:
© Copyright 1976
American Mathematical Society