We introduce a notion of topological extension of a given set X. The resulting class of topological spaces includes the Stone-ˇCech compactification βX of the discrete space X, as well as all nonstandard models of X in the sense of nonstandard analysis (when endowed with a “natural” topology). In this context, we give a simple characterization of nonstandard extensions in purely topological terms, and we establish connections with special classes of ultrafilters whose existence is independent of ZFC.

Topological and nonstandard extensions

DI NASSO, MAURO;FORTI, MARCO
2005-01-01

Abstract

We introduce a notion of topological extension of a given set X. The resulting class of topological spaces includes the Stone-ˇCech compactification βX of the discrete space X, as well as all nonstandard models of X in the sense of nonstandard analysis (when endowed with a “natural” topology). In this context, we give a simple characterization of nonstandard extensions in purely topological terms, and we establish connections with special classes of ultrafilters whose existence is independent of ZFC.
2005
DI NASSO, Mauro; Forti, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/184137
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