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Characterisation of compactness through convergence in Tychonoff spaces

Author(s): C. G. Petalas; T. Vidalis
Journal: Proc. Amer. Math. Soc. 124 (1996), 633-636.
MSC (1991): Primary 54A20, 54C35, 54D30
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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:

1: R. Engelking, General topology, PWN, Warzawa, 1977. MR 58:18316b
2: J. Ewert, Almost uniform convergence, Period. Math. Hungar. 26 (1993), 77--84. MR 94d:54008
3: J. Nagata, Modern general topology, North-Holland, Amsterdam, 1985. MR 87g:54003
4: M. Predoi, Sur la convergence quasi-uniforme, Period. Math. Hungar. 10 (1979), 31--40. MR 80a:54020
5: A. Wilansky, Topology for analysis, Wiley, New York, 1970.


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