If K is Gul'ko compact, then every iterated function space C-p,C-n (K) has a uniformly dense subspace of countable pseudocharacter

摘要

We establish that C-p(X) has a dense subspace of countable i-weight if and only if d(C-p(X)) = c. It is also proved that the space C-p(K) has a dense F-sigma-discrete subspace whenever K is Corson compact. If both spaces X and C-p(X) are Lindelof Sigma, then for any natural n = 2, the iterated function space C-p, (X) has a uniformly dense subspace of countable pseudocharacter. In the case of a Gul'ko compact space K, there is a uniformly dense subspace of countable pseudocharacter in C-p,C-n (K) for any n is an element of N. This is a new result even for C-p (K) given that K is Eberlein compact. (C) 2018 Elsevier Inc. All rights reserved.