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

Bar-Ilan University

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1016/j.topol.2019.106942

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title = "Strongly sequentially separable function spaces, via selection principles",

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.",

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AU - Szewczak, Piotr

AU - Tsaban, Boaz

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N2 - 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.

AB - 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.

KW - (ΩΓ)

KW - Borel function

KW - C-Space

KW - Function spaces

KW - Gerlits–Nagy

KW - Selection principles

KW - Strong sequential separability

KW - γ-Property

KW - γ-Set

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DO - 10.1016/j.topol.2019.106942

M3 - مقالة

SN - 0166-8641

VL - 270

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 106942

ER -

Strongly sequentially separable function spaces, via selection principles

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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