On LΣ(n)-spaces: Gδ-points and tightness

We prove that every LΣ(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 LΣ(n)-space has a dense set of Gδ-points, and every LΣ(n)-topological group has countable network.