On -spaces: -points and tightness

We prove that every L Σ ( 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 Σ ( n ) -space has a dense set of G δ -points, and every L Σ ( n ) -topological group has countable network.