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First countable extensions of regular spaces


Authors: Petr Simon and Gino Tironi
Journal: Proc. Amer. Math. Soc. 132 (2004), 2783-2792
MSC (2000): Primary 54D35; Secondary 54E30, 54D25, 54D80
DOI: https://doi.org/10.1090/S0002-9939-04-07408-8
Published electronically: March 25, 2004
MathSciNet review: 2054805
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate feebly compact extensions of first countable regular locally feebly compact spaces. Solutions of problems posed by R. M. Stephenson, Jr. and G. M. Reed are given.


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

  • [B] Murray G. Bell, First countable pseudocompactifications, Topology Appl. 21 (1985), 159 - 166. MR 87b:54019
  • [E] Ryszard Engelking, General Topology, Heldermann Verlag, Berlin (1989). MR 91c:54001
  • [GJ] Leonard Gillman and Meyer Jerison, Rings of Continuous Functions, Van Nostrand, Princeton, NJ (1960). MR 22:6994
  • [R1] George M. Reed, On chain conditions in Moore spaces, General Topology and Appl. 4 (1974), 255 - 267. MR 49:9815
  • [R2] George M. Reed, On subspaces of separable first countable T$_{2}$-spaces, Fund. Math. 91 (1976), 189 - 202. MR 54:13863
  • [R3] George M. Reed, Set-theoretic problems in Moore spaces, in: Open Problems in Topology, edited by J. van Mill and G. M. Reed, North-Holland, Amsterdam, 1990, 163 - 181. MR 92c:54001
  • [S] Robert M. Stephenson, Jr., Moore-closed and first countable feebly compact extension spaces, Topology Appl. 27 (1987), 11 - 28. MR 89g:54034
  • [TT] Toshiji Terada and Jun Terasawa, Maximal extensions of first-countable spaces, Proc. Amer. Math. Soc. 85 (1) (1982), 95 - 99. MR 84a:54042
  • [T] Ian J. Tree, Extending the discrete finite chain condition, Topology Appl. 52 (1993), 267 - 278. MR 95d:54018
  • [W] W. Stephen Watson, A connected pseudocompact space, Topology Appl. 57 (1994), 151 - 162. MR 95g:54001

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Additional Information

Petr Simon
Affiliation: Department of Computer Science and Mathematical Logic, Charles University, Malostranské nám. 25, 11000 Praha 1, Czech Republic
Email: psimon@ms.mff.cuni.cz

Gino Tironi
Affiliation: Dipartimento di Matematica, Università di Trieste, Via Alfonso Valerio 12/1, I-34127 Trieste, Italy
Email: tironi@univ.trieste.it

DOI: https://doi.org/10.1090/S0002-9939-04-07408-8
Keywords: Feebly compact space, Moore space, first countable space, extension
Received by editor(s): October 3, 2002
Received by editor(s) in revised form: May 26, 2003
Published electronically: March 25, 2004
Additional Notes: The authors gratefully acknowledge support provided by grants GAČR 201/00/1467 and GAUK 270/2001 (P. Simon) and by research funds of the University of Trieste (ex 60%) and of the “Real Analysis” PRIN group of MIUR (G. Tironi)
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society

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