Separately continuous mappings with values in nonlocally convex spaces

We prove that a collection (X, Y, Z) is a Lebesgue triple if X is a metrizable space, Y is a perfectly normal space, and Z is a strongly σ-metrizable topological vector space with stratification (Z _m) _{m = 1}^∞, where, for every m ∈ ℕ, Z _m is a closed, metrizable, separable subspace of Z that is arcwise connected and locally arcwise connected. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1639–1646, December, 2007.