Vol. 35, No. 2, 1970

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Gelfand and Wallman-type compactifications

Charles Morgan Biles

Vol. 35 (1970), No. 2, 267–278

In this paper we compare the Gelfand and Wallman methods of constructing a compactification for a Tychonoff space X from a suitable ring of continuous real-valued functions on X. Every Hausdorff compactification T of X is Gelfand constructable; in particular, T is equivalent, as a compactification of X, to the structure space of all maximal ideals of the ring of all continuously extendable functions from X to T. However, Wallman’s method applied to this ring may not yield T. We thus inquire into some relationships that exist between the Wallman and Gelfand compactification of X constructed from a suitable ring of functions on X.

Mathematical Subject Classification
Primary: 54.53
Received: 11 September 1969
Published: 1 November 1970
Charles Morgan Biles