Abstract:
Stratifiable spaces are a natural generalization of metrizable spaces for which Dugundji's theorem holds. It is proved that the free locally convex space
of a stratifiable space is stratifiable. This means, in particular,
that the space of finitely supported probability measures on a stratifiable space is a retract of a locally convex space, and
that each stratifiable convex subset of a locally convex space is a retract of a locally convex space.
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