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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Singular sets and maximal topologies


Authors: G. J. Kennedy and S. D. McCartan
Journal: Proc. Amer. Math. Soc. 127 (1999), 3375-3382
MSC (1991): Primary 54A10, 54F65; Secondary 54D80, 54D05
Published electronically: May 4, 1999
MathSciNet review: 1605984
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Abstract: Spaces which are maximal with respect to a semi-regular property are characterised. Furthermore, a method to construct such topologies is given. Consequently, new characterisations of maximal pseudocompact spaces and of maximal Q.H.C. spaces are presented. Known characterisations of maximal connected spaces and of maximal feebly compact spaces are given alternative proofs.


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Additional Information

G. J. Kennedy
Affiliation: Department of Pure Mathematics, Queen’s University of Belfast, Belfast BT7 1NN, Northern Ireland
Email: g.kennedy@qub.ac.uk

S. D. McCartan
Affiliation: Department of Pure Mathematics, Queen’s University of Belfast, Belfast BT7 1NN, Northern Ireland
Email: D.McCartan@qub.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04883-2
PII: S 0002-9939(99)04883-2
Keywords: Semi-regular property, singular set, submaximal, maximal connected, maximal pseudocompact, maximal quasi-H-closed, maximal feebly compact
Received by editor(s): May 28, 1997
Received by editor(s) in revised form: January 21, 1998
Published electronically: May 4, 1999
Additional Notes: The research of the first author was supported by a distinction award scholarship from the Department of Education for Northern Ireland.
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society