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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Characterisation of compactness through convergence in Tychonoff spaces
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by C. G. Petalas and T. Vidalis PDF
Proc. Amer. Math. Soc. 124 (1996), 633-636 Request permission

Abstract:

In this article we first give a characterisation of compact spaces among $T_{3.5}$ spaces by improving a theorem of J. Ewert. Then, with the aid of a new type of convergence, we give a characterisation of the pseudocompact and of the Lindelöf $T_{3.5}$ spaces.
References
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  • J. Ewert, Almost uniform convergence, Period. Math. Hungar. 26 (1993), no. 1, 77–84. MR 1230566, DOI 10.1007/BF01875883
  • Jun-iti Nagata, Modern general topology, 2nd ed., North-Holland Mathematical Library, vol. 33, North-Holland Publishing Co., Amsterdam, 1985. MR 831659
  • Maria Predoi, Sur la convergence quasi-uniforme, Period. Math. Hungar. 10 (1979), no. 1, 31–40 (French). MR 506165, DOI 10.1007/BF02018370
  • A. Wilansky, Topology for analysis, Wiley, New York, 1970.
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Additional Information
  • C. G. Petalas
  • Affiliation: Department of Mathematics, University of Ioannina, Ioannina, Greece
  • Email: cpetalas@cc.uoi.gr
  • T. Vidalis
  • Affiliation: Department of Mathematics, University of Ioannina, Ioannina, Greece
  • Email: vidalis@cc.uoi.gr
  • Received by editor(s): July 6, 1994
  • Communicated by: Franklin D. Tall
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 633-636
  • MSC (1991): Primary 54A20, 54C35, 54D30
  • DOI: https://doi.org/10.1090/S0002-9939-96-03414-4
  • MathSciNet review: 1328370