A remark on irreducible spaces
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- by J. C. Smith
- Proc. Amer. Math. Soc. 57 (1976), 133-139
- DOI: https://doi.org/10.1090/S0002-9939-1976-0405353-2
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Abstract:
A topological space $X$ is called irreducible if every open cover of $X$ has an open refinement which covers $X$ minimally. In this paper we show that weak $\bar \theta$-refinable spaces are irreducible. A modification of the proof of this result then yields that ${\aleph _1}$-compact, weak $\overline {\delta \theta }$-refinable spaces are Lindelöf. It then follows that perfect, ${\aleph _1}$-compact weak $\delta \theta$-refinable spaces are irreducible. A number of known results follow as corollaries.References
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Bibliographic Information
- © Copyright 1976 American Mathematical Society
- 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