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Separability and minimal weak base topologies


Authors: S. W. Davis and R. M. Stephenson
Journal: Proc. Amer. Math. Soc. 74 (1979), 371-378
MSC: Primary 54D25; Secondary 54E25, 54E30
DOI: https://doi.org/10.1090/S0002-9939-1979-0524320-4
MathSciNet review: 524320
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Abstract: In this note, we present filter characterizations of minimal weakly first countable, minimal $ \mathcal{F}$, minimal $ {\mathcal{F}_r}$, weakly first countable-closed, $ \mathcal{F}$-closed, and $ {\mathcal{F}_r}$-closed spaces. Our main result is a generalization of G. M. Reed's theorem that every Moore-closed space is separable.


References [Enhancements On Off] (What's this?)

  • [A] A. V. Arhangel'skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), 115-162. MR 0227950 (37:3534)
  • [C] Douglas E. Cameron, A survey of maximal topological spaces, Eleventh Annual Spring Topology Conference, Baton Rouge, Louisiana, 1977. MR 540596 (80k:54034)
  • [D] S. W. Davis, On $ {\mathcal{F}_r}$-spaces, General Topology and Appl. 9 (1978), 131-138. MR 0493961 (58:12912)
  • [DGN] S. W. Davis, G. Gruenhage and P. J. Nyikos, $ {G_\delta }$-sets in symmetrizable and related spaces, General Topology and Appl. 9 (1978), 253-261. MR 510907 (80a:54052)
  • [G] J. W. Green, Moore-closed spaces, completeness, and centered bases, General Topology and Appl. 4 (1974), 297-313. MR 0365502 (51:1754)
  • [HS] Peter W. Harley III and R. M. Stephenson, Jr., Symmetrizable and related spaces, Trans. Amer. Math. Soc. 219 (1976), 89-111. MR 0418048 (54:6092)
  • [M] R. A. McCoy, A filter characterization of regular Baire spaces, Proc. Amer. Math. Soc. 40 (1973), 268-270. MR 0339096 (49:3859)
  • [R] G. M. Reed, On chain conditions in Moore spaces, General Topology and Appl. 4 (1974), 255-267. MR 0345076 (49:9815)
  • [S$ _{1}$] R. M. Stephenson, Jr., Minimal first countable topologies, Trans. Amer. Math. Soc. 138 (1969), 115-127. MR 0238261 (38:6537)
  • [S$ _{2}$] -, Symmetrizable-closed spaces, Pacific J. Math. 68 (1977), 507-514. MR 0482678 (58:2735)
  • [S$ _{3}$] -, Symmetrizable, $ \mathcal{F}$-, and weakly first countable spaces, Canad. J. Math. 29 (1977), 480-488. MR 0442885 (56:1260)
  • [S$ _{4}$] -, Near compactness and separability of symmetrizable spaces, Proc. Amer. Math. Soc. 68 (1978), 108-110. MR 0458372 (56:16575)
  • [W] Stephen Willard, General topology, Addison-Wesley, Reading, Mass., 1970. MR 0264581 (41:9173)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0524320-4
Keywords: Weakly first countable, $ \mathcal{F}$-space, $ {\mathcal{F}_r}$-space, feebly compact, Baire space
Article copyright: © Copyright 1979 American Mathematical Society

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