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Topology and its ApplicationsVolume 270, 1 February 2020, Article number 106942

Strongly sequentially separable function spaces, via selection principles(Article)(Open Access)

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  • aKrasovskii Institute of Mathematics and Mechanics, Ural Federal University, Ural State University of Economics, Yekaterinburg, 620219, Russian Federation
  • bInstitute of Mathematics, Faculty of Mathematics and Natural Science, College of Sciences, Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland
  • cDepartment of Mathematics, Bar-Ilan University, Ramat Gan, Israel

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. © 2019 Elsevier B.V.

Author keywords

(ΩBorΓ)(ΩΓ)Borel functionC-SpaceFunction spacesGerlits–NagySelection principlesStrong sequential separabilityγ-Propertyγ-Set
  • ISSN: 01668641
  • CODEN: TIAPD
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1016/j.topol.2019.106942
  • Document Type: Article
  • Publisher: Elsevier B.V.

  Tsaban, B.; Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel;
© Copyright 2019 Elsevier B.V., All rights reserved.

Cited by 2 documents

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Unbounded towers and products
(2021) Annals of Pure and Applied Logic
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