Selectivity properties of spaces

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 $\mathbb{Q}$-selective from $\mathfrak{d}={\omega }_1$, and an $L$-selective space which is not selective for a $P$-point ultrafilter from the assumption of $\mathsf{CH}$. We also produce $\mathsf{ZFC}$ examples of Fréchet spaces where countable subsets are first countable which are not $L$-selective.

References in corpus (1)

• Continuous Selections of Lower semicontinuous Set-valued Mappings