Observations about equicontinuity and related concepts

Abstract

The concepts of equicontinuity, even continuity, topological equicontinuity and the newly defined concepts of compact equicontinuity and compact topological equicontinuity are compared. It is shown that for a set of group homomorphisms from a semitopological group to a topological group all these notions of equicontinuities coincide. It is shown also that an infinite-dimensional normed space endowed with its weak topology is an example of a space which does not satisfy the Ascoli theorem in Noble's sense.

Equicontinuity, transitivity and sensitivity: The Auslander-Yorke dichotomy revisited

“…Whilst the concepts of topological equicontinuity and even continuity have gained some attention with regard to topological semigroups and families of mappings in a general setting (e.g. [5,6]), little appears to have been done with regard to dynamical systems.…”