More nondevelopable spaces in $\textrm {MOBI}$
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- by J. Chaber PDF
- Proc. Amer. Math. Soc. 103 (1988), 307-313 Request permission
Abstract:
We construct two spaces with a point-countable base, the first is not weakly $\theta$-refinable, while the second is not a ${\sigma ^\# }$-space. Both spaces can be represented as open and compact images of metacompact developable Hausdorff spaces. This answers questions of H. R. Bennett and R. F. Gittings.References
- C. E. Aull, Topological spaces with a $\sigma$-point finite base, Proc. Amer. Math. Soc. 29 (1971), 411–416. MR 281154, DOI 10.1090/S0002-9939-1971-0281154-9
- H. R. Bennett, On Arhangel′skiĭ’s class $\textrm {MOBI}$, Proc. Amer. Math. Soc. 26 (1970), 178–180. MR 267523, DOI 10.1090/S0002-9939-1970-0267523-0
- Harold R. Bennett, On quasi-developable spaces, General Topology and Appl. 1 (1971), no. 3, 253–262. MR 288725, DOI 10.1016/0016-660X(71)90096-1
- H. R. Bennett, On open-compact images of metacompact spaces, Topology Proc. 4 (1979), no. 2, 339–343 (1980). MR 598278
- H. R. Bennett and D. J. Lutzer, A note on weak $\theta$-refinability, General Topology and Appl. 2 (1972), 49–54. MR 301697, DOI 10.1016/0016-660X(72)90035-9
- J. Chaber, Metacompactness and the class MOBI, Fund. Math. 91 (1976), no. 3, 211–217. MR 415561, DOI 10.4064/fm-91-3-211-217 —, Primitive generalizations of $\sigma$-spaces, Colloq. Math. Soc. János Bolyai 23, Topology, Budapest, 1978, pp. 259-268.
- S. W. Davis, A nondevelopable Čech-complete space with a point-countable base, Proc. Amer. Math. Soc. 78 (1980), no. 1, 139–142. MR 548102, DOI 10.1090/S0002-9939-1980-0548102-0
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- William G. Fleissner, Left separated spaces with point-countable bases, Trans. Amer. Math. Soc. 294 (1986), no. 2, 665–677. MR 825729, DOI 10.1090/S0002-9947-1986-0825729-X
- Raymond F. Gittings, Open mapping theory, Set-theoretic topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975–1976) Academic Press, New York, 1977, pp. 141–191. MR 0482628
- Gary Gruenhage, On a Corson compact space of Todorčević, Fund. Math. 126 (1986), no. 3, 261–268. MR 882434, DOI 10.4064/fm-126-3-261-268
- G. Gruenhage and R. J. Gardner, Completeness and weak covering properties, and measure-compactness, J. London Math. Soc. (2) 18 (1978), no. 2, 316–324. MR 509947, DOI 10.1112/jlms/s2-18.2.316
- Heikki J. K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), no. 1, 83–108. MR 482677, DOI 10.2140/pjm.1978.76.83 —, Stratifiable preimages of topological spaces, Colloq. Math. Soc. János Bolyai 23, Topology, Budapest, 1978, pp. 689-703.
- E. Michael, A note on completely metrizable spaces, Proc. Amer. Math. Soc. 96 (1986), no. 3, 513–522. MR 822451, DOI 10.1090/S0002-9939-1986-0822451-6 A. Miščenko, Spaces with point-countable base, Dokl. Akad. Nauk SSSR 144 (1962), 985-988.
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 307-313
- MSC: Primary 54C10; Secondary 54D18
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938688-3
- MathSciNet review: 938688