This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from into the hyperspace of closed nonempty subsets of admit a continuous selection?

We construct a space which is $L$-selective but not $\mathbb{Q}$-selective from $\mathfrak{d}=\aleph_1$, and an $L$-selective space which is not selective for a $P$-point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not $L$-selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.