On spaces of Baire I functions over K-analytic spaces

Suppose that 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 of is a strongly countably compact Frechét-Urysohn space; (2) if is ₁ -compact, is a bicompactum; (3) if X is a paracompact space, the closure of is a bicompactum.Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 108–116, September, 1992.