On L∑(n)-spaces: G_δ-points and tightness

摘要

We prove that every L∑(n)-space (that is, the image of a separable metrizable space under an at most n-valued upper semicontinuous mapping) is a union of n subspaces of countable pseudocharacter and has countable tightness. In particular, every L∑(n)-space has a dense set of G_δ-points, and every L∑(n)-topological group has countable network.