Few remarks on maximal pseudocompactness

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.

Downloads

Download data is not yet available.

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

Downloads

Published

2018-04-02

How to Cite

[1]
A. Bella, “Few remarks on maximal pseudocompactness”, Appl. Gen. Topol., vol. 19, no. 1, pp. 155–161, Apr. 2018.

Issue

Section

Articles