Equicontinuity criteria for metric-valued sets of continuous functions

TL;DR

This paper provides new criteria for almost equicontinuity and hereditary almost equicontinuity of metric-valued continuous functions on ech-complete spaces, with applications to topological groups and dynamical systems.

Contribution

It introduces several new characterizations of almost equicontinuity and hereditary almost equicontinuity for function sets on ech-complete spaces, extending previous ideas.

Findings

Characterizations of almost equicontinuity for metric-valued functions

Criteria for hereditary almost equicontinuity

Applications to topological groups and dynamical systems

Abstract

Combining ideas of Troallic and Cascales, Namioka, and Vera, we prove several characterizations of \textit{almost equicontinuity} and \textit{hereditary almost equicontinuity} for subsets of metric-valued continuous functions when they are defined on a \v{C}ech-complete space. We also obtain some applications of these results to topological groups and dynamical systems.