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Nonstandard topological extensions

Published online by Cambridge University Press:  17 April 2009

Robert A. Herrmann
Robert A. Herrmann
Affiliation:
Department of Mathematics, US Naval Academy, Annapolis, Maryland, USA.
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Abstract

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This paper investigates the nonstandard theory of filters on a non-empty meet-semi-lattice of sets and applies this theory to the general study of topological extensions Y for a space X. In particular, we apply this theory to Baire and quasi-H-closed extensions as well as Wallman type compactifications. Whereas these extensions have previously teen obtained and studied as types of ultrafilter extensions, we study them as subsets of an enlargement of X. Since X ⊂ Y ⊂ ◯ and the elements of X and Y - X are of the same set-theoretic type, these extensions appear more natural from the nonstandard viewpoint.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 2 , October 1975 , pp. 269 - 290
Copyright
Copyright © Australian Mathematical Society 1975

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