A Banach space characterization of (sequentially) Ascoli spaces

Saak Gabriyelyan

A Banach space characterization of (sequentially) Ascoli spaces

Functional Analysis 2023-07-24 v1 General Topology

Authors: Saak Gabriyelyan

Abstract

We prove that a Tychonoff space $X$ is an Ascoli space (resp., a sequentially Ascoli space) if and only if for each Banach space $E$ , every $k$ -continuous and almost $k$ -compact (resp., almost $k$ -sequential) map $T$ form $X$ into the Banach dual $E'$ of $E$ is continuous.

Keywords

tychonoff space ascoli space sequentially ascoli space banach space k-continuous map almost k-compact map

Cite

@article{arxiv.2307.11561,
  title  = {A Banach space characterization of (sequentially) Ascoli spaces},
  author = {Saak Gabriyelyan},
  journal= {arXiv preprint arXiv:2307.11561},
  year   = {2023}
}

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