A Banach space characterization of (sequentially) Ascoli spaces

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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.

Original languageEnglish
Article number108748
JournalTopology and its Applications
Volume341
DOIs
StatePublished - 1 Jan 2024

Keywords

  • Ascoli space
  • k-continuous map
  • Sequentially Ascoli space

ASJC Scopus subject areas

  • Geometry and Topology

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