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Nonstandard topological extensions: Addendum
Published online by Cambridge University Press: 17 April 2009
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It has recently come to my attention that, independent from my investigations in [1], Professor K.D. Stroyan [2] obtains for a Tychonoff space X and a normal base β a quotient space on *X which is homeomorphic to the Wallman-Frink Hausdorff compactification w(X, β). Consequently, if X is Tychonoff, then Corollary 4.1 in [1] implies that Stroyan's space is homeomorphic to the space w(X, β)S which is constructed in Theorem 4.1 in [1]. Stroyan's result is obtained by use of a monadic closure operator.
I regret not mentioning Professor Stroyan's result in my paper [1].
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- Addendum
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- Copyright © Australian Mathematical Society 1975
References
[1]Herrmann, Robert A., “Nonstandard topological extensions”, Bull. Austral. Math. Soc. 13 (1975), 269–290.CrossRefGoogle Scholar
[2]Stroyan, K.D., “Additional remarks on the theory of monads”, Contributions to non-standard analysis, 245–259 (Studies in Logic and the Foundations of Mathematics, 69. North-Holland, Amsterdam, London, 1972).CrossRefGoogle Scholar
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