Weak local homeomorphisms and B-favorable spaces

Abstract

Let X and Y be topological spaces such that every mapping f : X → Y for which the set f ^{- 1}(G) is an f _σ -set in X for any set G open in Y can be represented as a pointwise limit of continuous mappings f_n : X → Y. The question of subspaces Z of the space Y for which mappings f : X → Z have the same property is investigated.