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¿Question #222590?
TomTi89: Have you heard of the Michael selection theorem?

pricero1: He selects only the best okra to fry.
TomTi89: @Michael: Well, I know some of these words, but by no means all of them: "In functional analysis, a branch of mathematics, Michael selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following:[1] Let X be a paracompact space and Y a Banach space. Let F : X → Y {\displaystyle F\colon X\to Y} {\displaystyle F\colon X\to Y} be a lower hemicontinuous multivalued map with nonempty convex closed values. Then there exists a continuous selection f : X → Y {\displaystyle f\colon X\to Y} f\colon X\to Y of F. Conversely, if any lower semicontinuous multimap from topological space X to a Banach space, with nonempty convex closed values, admits a continuous selection, then X is paracompact. This provides another characterization for paracompactness."
PolarDad: I have not. Tell me more.