Abstract
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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1639–1646, December, 2007.
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Karlova, O.O., Maslyuchenko, V.K. Separately continuous mappings with values in nonlocally convex spaces. Ukr Math J 59, 1840–1849 (2007). https://doi.org/10.1007/s11253-008-0029-4
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DOI: https://doi.org/10.1007/s11253-008-0029-4