Maximal perfect spaces

Publisher： Cambridge University Press

E-ISSN： 1755-1633|7|3|429-436

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.7, Iss.3, 1972-12, pp. : 429-436

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Abstract

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.

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