Paper read at the Symposium on Categorical Algebra and Topology University of Cape Town 29 June—3 July 1981

REAL COMPACTIFICATIONS THROUGH ZERO-SET SPACES

Published in: Quaestiones Mathematicae
Volume 6 , issue 1-3 , 1983 , pages: 73–95

DOI: 10.1080/16073606.1983.9632293

Author(s): Christopher , R.A. Gilmour Department of Mathematics,

Keywords: Primary 54D60 , 54C50 , Secondary 54E99 , 54B10

Abstract

The Alexandroff (= zero-set) spaces were introduced in [l] as the “completely normal spaces”, and have been studied in a number of more recent papers. In this paper we unify the theory of Wallman realcompactifications via the Alexandroff bases and introduce the realcompactfine Alexandroff spaces as particularly relevant to their investigation. These latter spaces are defined analogously to the A-c uniform spaces which are based on a construction of A.W. Hager [25].

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