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Maximal extensions of first-countable spaces

Authors: Toshiji Terada and Jun Terasawa
Journal: Proc. Amer. Math. Soc. 85 (1982), 95-99
MSC: Primary 54D20; Secondary 54C20
MathSciNet review: 647906
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Abstract: A first-countable space is called maximal if it is not contained as a dense subspace in a first-countable space properly. The following are shown; (1) every locally compact, first-countable space is a dense subspace of a maximal space, (2) every metrizable space is a dense subspace of a maximal space, and (3) there is a first-countable space which is not a dense subspace of any maximal space.

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  • [A] A. V. Arhangel'skiĭ, Structure and classification of topological spaces and cardinal invariants, Uspehi Mat. Nauk 33 (1978), no. 6, 29-84 = Russian Math. Surveys 33 (1978), no. 6, 33-96. MR 526012 (80i:54005)
  • [vDP] E. K. van Douwen and T. C. Przymuśinski, First-countable and countable spaces all compactifications of which contain $ \beta N$, Fund. Math. 102 (1979), 229-234. MR 532957 (80e:54031)
  • [E] R. Engelking, General topology, PWN, Warsaw, 1977. MR 0500780 (58:18316b)
  • [N] J. Nagata, Modern general topology, North-Holland, Amsterdam, 1968.
  • [S] R. M. Stephenson, Jr., Minimal first countable topologies, Trans. Amer. Math. Soc. 138 (1969), 115-127. MR 0238261 (38:6537)
  • [T] J. Terasawa, Spaces $ N \cup \mathcal{R}$ and their dimensions, Topology Appl. 11 (1980), 93-102. MR 550876 (82k:54040)
  • [W] R. Walker, The Stone-Čech compactification, Springer-Verlag, Berlin, Heidelberg and New York, 1974. MR 0380698 (52:1595)

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Keywords: First-countable, pseudocompact, maximal extension, locally compact, metrizable, Čech-complete
Article copyright: © Copyright 1982 American Mathematical Society

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