Projective versions of the properties in the Scheepers Diagram

Alexander V. Osipov

Projective versions of the properties in the Scheepers Diagram

General Topology 2020-05-06 v2

Authors: Alexander V. Osipov

Abstract

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

Keywords

projective topological property scheepers diagram selection properties covering properties continuous images second countable functional characterization

Cite

@article{arxiv.1812.05925,
  title  = {Projective versions of the properties in the Scheepers Diagram},
  author = {Alexander V. Osipov},
  journal= {arXiv preprint arXiv:1812.05925},
  year   = {2020}
}

Comments

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

Projective versions of the properties in the Scheepers Diagram

Abstract

Keywords

Cite

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