Selectivity properties of spaces

2019/10/23 by Chen-Mertens, William, Szeptycki, Paul J.
#54A20 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1910.10634

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 L-selective but not ℚ-selective from \mathfrakd=ω₁, and an L-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 L-selective.

Related

• Continuous Selections of Lower semicontinuous Set-valued Mappings
• Dense families of selections and finite-dimensional spaces
• New examples in the study of selectively separable spaces
• k-spaces, sequential spaces and related topics in the absence of the axiom of choice
• Selectively pseudocompact spaces