Universal maps and surjective characterizations of completely metrizable 𝐿𝐶ⁿ-spaces

Abstract

Abstract.We construct an «-dimensional completely metrizable ^4£'(«)-space P(n, t) of weight r > ca with the following property: for any at most ndimensional completely metrizable space Y of weight < t the set of closed embeddings Y -» P(n , t) is dense in the space C(Y, P(n , x)) . It is also shown that completely metrizable LC" -spaces of weight t > w are precisely the H-invertible images of the Hilbert space (2(r) .