A non-metrizable compact linearly ordered topological space, every subspace of which has a $\sigma$-minimal base
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Abstract:
A collection $\mathcal {D}$ of subsets of a space is minimal if each element of $\mathcal {D}$ contains a point which is not contained in any other element of $\mathcal {D}$. A base of a topological space is $\sigma$-minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space $X$ satisfying that $X$ is not metrizable and every subspace of $X$ has a $\sigma$-minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.References
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Additional Information
- Wei-Xue Shi
- Affiliation: Department of Mathematics, Changchun Teachers College, Changchun 130032, China
- Address at time of publication: Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305, Japan
- Email: shi@abel.math.tsukuba.ac.jp
- Received by editor(s): October 25, 1996
- Received by editor(s) in revised form: November 15, 1997
- Published electronically: April 15, 1999
- Communicated by: Alan Dow
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2783-2791
- MSC (1991): Primary 54F05, 54G20, 54E35
- DOI: https://doi.org/10.1090/S0002-9939-99-04853-4
- MathSciNet review: 1600133