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Maximal perfect spaces

Published online by Cambridge University Press:  17 April 2009

Ivan Baggs
Ivan Baggs
Affiliation:
St Francis Xavier University, Antigonish, Nova Scotia, Canada.
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Abstract

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Let (X, T) be a topological space (we assume T1. throughout) where every point is a limit point. The purpose of this note is to present an internal construction of a maximal perfect topology on (X, T). The existence of a maximal connected Hausdorff space has not been demonstrated. However, this construction of a maximal perfect topology is useful in constructing connected Hausdorff spaces which cannot be embedded in a maximal connected Hausdorff space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 429 - 436
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Baggs, Ivan, “A connected Hausdorff space vhich is not contained in a maximal connected space”, (to appear).Google Scholar
[2]Thomas, J. Pelham, “Maximal connected topologies”, J. Austral. Math. Soc. 8 (1968), 700–705.CrossRefGoogle Scholar