Nonstandard topological extensions

Abstract

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 extensionsYfor a spaceX.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 ofX.SinceX⊂Y⊂ ◯ and the elements ofXandY-Xare of the same set-theoretic type, these extensions appear more natural from the nonstandard viewpoint.