Projective versions of the properties in the Scheepers Diagram

2018/12/13 by Alexander V. Osipov, Osipov, Alexander V.
Mathematics · #Advanced Topology and Set Theory #Artificial intelligence #Combinatorics #Computer science #Countable set #Diagram #Discrete mathematics #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Image (mathematics) #Limits and Structures in Graph Theory #Mathematics #Omega #Physics #Projective test #Pure mathematics #Topology (electrical circuits) #math.GN

paper · pdf · doi:10.48550/arxiv.1812.05925

30 pages, 3 figures. arXiv admin note: text overlap with arXiv:1708.06404, arXiv:1710.07272, arXiv:1805.11019

openalex publication_date 2018/12/13 · arxiv created 2020/05/05 · arxiv updated 2020/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let P be a topological property. A.V. Arhangel'skii calls X projectively P if every second countable continuous image of X is P. Lj.D.R. Ko\checkcinac characterized the classical covering properties of Menger, Rothberger, Hurewicz and Gerlits-Nagy in term of continuous images in ℝ^ω. In this paper we study the functional characterizations of all projective versions of the selection properties in the Scheepers Diagram.

Citations

• Classification of selectors for sequences of dense sets of Cp(X)
• Classification of selectors for sequences of dense sets of Baire functions
• The functional characteristics of the Rothberger and Menger properties

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