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.
|Autori:||DI NASSO M; FORTI M|
|Titolo:||Topological and nonstandard extensions|
|Anno del prodotto:||2005|
|Digital Object Identifier (DOI):||10.1007/s00605-004-0255-2|
|Appare nelle tipologie:||1.1 Articolo in rivista|