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On Hewitt's τ-maximal spaces

Published online by Cambridge University Press:  09 April 2009

Murray R. Kirch
Murray R. Kirch
Affiliation:
State University of New YorkBuffalo, U.S.A.
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Let τ be any cardinal number. Edwin Hewitt [3] has defined a topological space (X, J) to be τ-maximal if δ(J) ≥ τ and δ(J') < τ whenever J' is a topology for X which is strictly stronger that J (Δ denotes dispersion character, the least cardinality of a nonempty open set). The notion of an ℵ0-maximal space was introduced independently by Katětov [4].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 45 - 48
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Anderson, D. R., ‘On connected irresolvable Hausdorff spaces’, Proc. Amer. Math. Soc. 16 (1965), 463–466.CrossRefGoogle Scholar
[2]Bourbaki, N., Éléments de Mathématique, Topologie Générale Book III, Chap. 1 (Hermann, Paris, 1961).Google Scholar
[3]Hewitt, E., ‘A problem of set-theoretic topology’, Duke Math. J. 10 (1943), 309–333.CrossRefGoogle Scholar
[4]Katětov, M., ‘On topological spaces containing no disjoint dense sets’, Mat. Sb. (N.S.) 21 (1947), 3–12.Google Scholar
[5]Kirch, M. R., ‘Weakly equivaent topologies’, Bull. Acad. Polon. Sci. (to appear).Google Scholar
[6]Levine, N., ‘Simple extensions of topologies’, Amer. Math. Monthly 71 (1964), 22–25.CrossRefGoogle Scholar