SELECTIVITY PROPERTIES OF SPACES

William Chen-Mertens; Paul J. Szeptycki

SELECTIVITY PROPERTIES OF SPACES

William Chen-Mertens
, Paul J. Szeptycki

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

Abstract

This paper addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. We construct an example of a space which is (ω + 1)-selective but not ℚ-selective from d = ω₁, and an (ω + 1)-selective space which is not selective for a P-point ultrafilter from the assumption of CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not (ω + 1)-selective.

Original language	English
Pages (from-to)	61-76
Number of pages	16
Journal	Topology Proceedings
Volume	57
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

(ω+1)-selective
C-selective
Fréchet space
Set-valued mapping
continuous selection
tight gap

ASJC Scopus subject areas

Geometry and Topology

Cite this

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abstract = "This paper addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. We construct an example of a space which is (ω + 1)-selective but not ℚ-selective from d = ω1, and an (ω + 1)-selective space which is not selective for a P-point ultrafilter from the assumption of CH. We also produce ZFC examples of Fr{\'e}chet spaces where countable subsets are first countable which are not (ω + 1)-selective.",

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AB - This paper addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. We construct an example of a space which is (ω + 1)-selective but not ℚ-selective from d = ω1, and an (ω + 1)-selective space which is not selective for a P-point ultrafilter from the assumption of CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not (ω + 1)-selective.

KW - (ω+1)-selective

KW - C-selective

KW - Fréchet space

KW - Set-valued mapping

KW - continuous selection

KW - tight gap

UR - https://www.scopus.com/pages/publications/85156086321

M3 - Article

AN - SCOPUS:85156086321

SN - 0146-4124

VL - 57

SP - 61

EP - 76

JO - Topology Proceedings

JF - Topology Proceedings

ER -

SELECTIVITY PROPERTIES OF SPACES

Abstract

Keywords

ASJC Scopus subject areas

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