A note on Fortʼs theorem

Fortʼs theorem states that if F:X→2Y is an upper (lower) semicontinuous set-valued mapping from a Baire space (X,τ) into the nonempty compact subsets of a metric space (Y,d) then F is both upper and lower semicontinuous at the points of a dense Gδ subset of X. In this paper we show that a variant of Fortʼs theorem holds, without the assumption of the compactness of the images, provided we restrict the domain space of the mapping to a large class of “nice” Baire spaces.