A note on Fortʼs theorem

Fortʼs theorem states that if F : X → 2 Y 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 G δ 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.