Local completeness of Ck(X)

Saak Gabriyelyan

doi:https://doi.org/10.1007/s13398-023-01487-7

Local completeness of C_k(X)

Saak Gabriyelyan

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

Answering a long-standing open problem we characterize locally complete spaces C_k(X) , where C_k(X) denotes the space of all real-valued continuous functions on a Tychonoff space X endowed with the compact-open topology. We show that C_k(X) is locally complete if and only if every strongly functionally compact-finite sequence of functionally closed subsets of X is locally finite. For the important partial case when X is a pseudocompact space, we extend a classical result of Warner with an independent proof.

Original language	American English
Article number	152
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	117
Issue number	4
DOIs	https://doi.org/10.1007/s13398-023-01487-7
State	Published - 1 Oct 2023

Keywords

C(X)
Local completeness
Sequentially ascoli space

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology
Computational Mathematics
Applied Mathematics

Access to Document

https://doi.org/10.1007/s13398-023-01487-7

Cite this

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