Strongly sequentially separable function spaces, via selection principles

Alexander V. Osipov; Piotr Szewczak; Boaz Tsaban

doi:10.1016/j.topol.2019.106942

Strongly sequentially separable function spaces, via selection principles

Alexander V. Osipov
, Piotr Szewczak
, Boaz Tsaban

Department of Mathematics

Ural Federal University
Cardinal Stefan Wyszynski University

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

5 Scopus citations

Abstract

A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continuous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.

Original language	English
Article number	106942
Journal	Topology and its Applications
Volume	270
DOIs	https://doi.org/10.1016/j.topol.2019.106942
State	Published - 1 Feb 2020

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Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

(ΩΓ)
(ΩΓ)
Borel function
C-Space
Function spaces
Gerlits–Nagy
Selection principles
Strong sequential separability
γ-Property
γ-Set

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10.1016/j.topol.2019.106942

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KW - Function spaces

KW - Gerlits–Nagy

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KW - γ-Property

KW - γ-Set

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Strongly sequentially separable function spaces, via selection principles

Abstract

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Keywords

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