Let B be an ideal of subsets of a metric space 〈 X, d 〉. This paper considers a strengthening of the notion of uniform continuity of a function restricted to members of B which reduces to ordinary continuity when B consists of the finite subsets of X and agrees with uniform continuity on members of B when B is either the power set of X or the family of compact subsets of X. The paper also presents new function space topologies that are well suited to this strengthening. As a consequence of the general theory, we display necessary and sufficient conditions for continuity of the pointwise limit of a net of continuous functions. © 2008 Elsevier Inc. All rights reserved.
Beer, G., & Levi, S. (2009). Strong uniform continuity. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 350(2), 568-589.
Citazione: | Beer, G., & Levi, S. (2009). Strong uniform continuity. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 350(2), 568-589. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Strong uniform continuity |
Autori: | Beer, G; Levi, S |
Autori: | |
Data di pubblicazione: | 2009 |
Lingua: | English |
Rivista: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jmaa.2008.03.058 |
Appare nelle tipologie: | 01 - Articolo su rivista |