Strong uniform continuity

By Gerald Beer, S. Levi. 2009

110 citations recorded by the source corpus.

Abstract 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74b5d52bc7d98e5a862cd76c5ddb1adb44ef782f