Open AccessHausdorff Nonstandard Extensions
Author(s) -
Vieri Benci,
Marco Forti,
Mauro Di Nasso
Publication year - 2009
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v20i1-2.7519
Subject(s) - hausdorff space , compactification (mathematics) , mathematics , extension (predicate logic) , normal space , hausdorff distance , urysohn and completely hausdorff spaces , pure mathematics , hausdorff measure , hausdorff dimension , continuous functions on a compact hausdorff space , discrete mathematics , mathematical analysis , topological space , computer science , topological vector space , programming language
We introduce the notion of Hausdorff extension of an arbitrary set X and we study the connections with the Stone-Cech compactification *X of the discrete space X. We characterize those Hausdorff extensions that satisfy the "transfer principle" of nonstandard analysis, and we investigate the consistency strength of their existence