On spaces of Baire I functions over K-analytic spaces

Abstract

Suppose thatℱ is a relatively countably compact subset of B1(X), the space of Baire I functions over a K-analytic space X equipped with the pointwise convergence topology. It is proved that (1) the closure ofℱ is a strongly countably compact Frechet-Urysohn space; (2) ifℱ is ℵ1 -compact,ℱ is a bicompactum; (3) if X is a paracompact space, the closure ofℱ is a bicompactum.