On Distinguished Spaces Cp(X) of Continuous Functions

J. Ka̧kol; A. Leiderman

doi:https://doi.org/10.1007/978-3-031-30014-1_10

On Distinguished Spaces C_p(X) of Continuous Functions

J. Ka̧kol, A. Leiderman

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This survey paper presents a number of recent results related to the study of spaces C_p(X) of continuous real-valued functions on a Tychonoff spaces X with the pointwise topology that are distinguished, i.e. spaces C_p(X) which are large subspaces of R^X, equivalently, spaces C_p(X) whose strong dual L_β(X) of C_p(X) carries the finest locally convex topology. Some open questions are included.

Original language	American English
Title of host publication	Functional Analysis and Continuous Optimization - In Honour of Juan Carlos Ferrando’s 65th Birthday, 2022
Editors	José M. Amigó, María J. Cánovas, Marco A. López-Cerdá, Manuel López-Pellicer
Publisher	Springer
Pages	213-236
Number of pages	24
ISBN (Print)	9783031300134
DOIs	https://doi.org/10.1007/978-3-031-30014-1_10
State	Published - 1 Jan 2023
Event	International Meeting on Functional Analysis and Continuous Optimization, IMFACO 2022 - Elche, Spain Duration: 16 Jun 2022 → 17 Jun 2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	424

Conference

Conference	International Meeting on Functional Analysis and Continuous Optimization, IMFACO 2022
Country/Territory	Spain
City	Elche
Period	16/06/22 → 17/06/22

Keywords

Bidual space
Distinguished space
Eberlein compact space
Fré chet space
Point-finite family
Q-space
Strongly splittable space

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1007/978-3-031-30014-1_10

Cite this

Ka̧kol, J., & Leiderman, A. (2023). On Distinguished Spaces C_p(X) of Continuous Functions. In J. M. Amigó, M. J. Cánovas, M. A. López-Cerdá, & M. López-Pellicer (Eds.), Functional Analysis and Continuous Optimization - In Honour of Juan Carlos Ferrando’s 65th Birthday, 2022 (pp. 213-236). (Springer Proceedings in Mathematics and Statistics; Vol. 424). Springer. https://doi.org/10.1007/978-3-031-30014-1_10

Ka̧kol, J. ; Leiderman, A. / On Distinguished Spaces C_p(X) of Continuous Functions. Functional Analysis and Continuous Optimization - In Honour of Juan Carlos Ferrando’s 65th Birthday, 2022. editor / José M. Amigó ; María J. Cánovas ; Marco A. López-Cerdá ; Manuel López-Pellicer. Springer, 2023. pp. 213-236 (Springer Proceedings in Mathematics and Statistics).

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abstract = "This survey paper presents a number of recent results related to the study of spaces Cp(X) of continuous real-valued functions on a Tychonoff spaces X with the pointwise topology that are distinguished, i.e. spaces Cp(X) which are large subspaces of RX, equivalently, spaces Cp(X) whose strong dual Lβ(X) of Cp(X) carries the finest locally convex topology. Some open questions are included.",

keywords = "Bidual space, Distinguished space, Eberlein compact space, Fr{\'e} chet space, Point-finite family, Q-space, Strongly splittable space",

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Ka̧kol, J & Leiderman, A 2023, On Distinguished Spaces C_p(X) of Continuous Functions. in JM Amigó, MJ Cánovas, MA López-Cerdá & M López-Pellicer (eds), Functional Analysis and Continuous Optimization - In Honour of Juan Carlos Ferrando’s 65th Birthday, 2022. Springer Proceedings in Mathematics and Statistics, vol. 424, Springer, pp. 213-236, International Meeting on Functional Analysis and Continuous Optimization, IMFACO 2022, Elche, Spain, 16/06/22. https://doi.org/10.1007/978-3-031-30014-1_10

On Distinguished Spaces C_p(X) of Continuous Functions. / Ka̧kol, J.; Leiderman, A.
Functional Analysis and Continuous Optimization - In Honour of Juan Carlos Ferrando’s 65th Birthday, 2022. ed. / José M. Amigó; María J. Cánovas; Marco A. López-Cerdá; Manuel López-Pellicer. Springer, 2023. p. 213-236 (Springer Proceedings in Mathematics and Statistics; Vol. 424).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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KW - Bidual space

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KW - Eberlein compact space

KW - Fré chet space

KW - Point-finite family

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Ka̧kol J, Leiderman A. On Distinguished Spaces C_p(X) of Continuous Functions. In Amigó JM, Cánovas MJ, López-Cerdá MA, López-Pellicer M, editors, Functional Analysis and Continuous Optimization - In Honour of Juan Carlos Ferrando’s 65th Birthday, 2022. Springer. 2023. p. 213-236. (Springer Proceedings in Mathematics and Statistics). doi: https://doi.org/10.1007/978-3-031-30014-1_10