A Banach space characterization of (sequentially) Ascoli spaces

S. Gabriyelyan

doi:10.1016/j.topol.2023.108748

A Banach space characterization of (sequentially) Ascoli spaces

S. Gabriyelyan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Article number	108748
Journal	Topology and its Applications
Volume	341
DOIs	https://doi.org/10.1016/j.topol.2023.108748
State	Published - 1 Jan 2024

Keywords

Ascoli space
Sequentially Ascoli space
k-continuous map

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2023.108748

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title = "A Banach space characterization of (sequentially) Ascoli spaces",

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.",

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AB - 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.

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A Banach space characterization of (sequentially) Ascoli spaces

Abstract

Keywords

ASJC Scopus subject areas

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