Few remarks on maximal pseudocompactness

Angelo Bella

doi:10.4995/agt.2018.7888

Authors

Angelo Bella University of Catania

DOI:

https://doi.org/10.4995/agt.2018.7888

Keywords:

pseudocompact, maximal pseudocompact, hereditarily maximal pseudocompact, accessible set

Abstract

A pseudocompact space is maximal pseudocompact if every strictly finer topology is no longer pseudocompact. The main result here is a counterexample which answers a question rised by Alas, Sanchis and Wilson.

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Author Biography

Angelo Bella, University of Catania

Department of Mathematics and Computer Science

References

O. T. Alas, M. Sanchis and R. G. Wilson, Maximal pseudocompact and maximal R-closed spaces, Houston J. Math. 38 (2012), 1355-1367.

O. T. Alas, W. W. Tkachuk and R. G. Wilson, Maximal pseudocompact spaces and the Preiss-Simon property, Central Eur. J. Math. 12 (2014), 500-509. https://doi.org/10.2478/s11533-013-0359-9

E. K. van Douwen, The integers and topology, in: Handbook of Set-theoretic Topology (K. Kunen and J. E. Vaughan Editors), Elsevier Science Publishers B.V., Amsterdam, (1984), 111-160. https://doi.org/10.1016/B978-0-444-86580-9.50006-9

A. Dow, On compact separable radial spaces, Canad. Math. Bull. 40 (1997), 422-432. https://doi.org/10.4153/CMB-1997-050-0

R. Engelking, General topology, Heldermann Verlag, Berlin (1989).

P. J. Nyikos, Convergence in topology, in: Recent Progress in General Topology. Elsevier Science Publishers B. V. (Amsterdam). M. Husek and J. van Mill ed. (1992), 537-570.

K. M. Devi, P. R. Meyer and M. Rajagopalan, When does countable compactness imply sequential compactness?, General Topology Appl. 6 (1976), 279-289. https://doi.org/10.1016/0016-660X(76)90016-7

V. V. Tkachuk and R. G. Wilson, Maximal countably compact spaces and embeddings in MP spaces, Acta Math. Hungar. 145, no. 1 (2015), 191-204. https://doi.org/10.1007/s10474-014-0469-2