Spaces with a Souslin and a shanin condition

Abstract

If X is a regular hereditary Souslin space and x ∈X then either there exists a sequence {xn: n=1, 2, ...} ⊂ X{x} such that x ∈ [{xn∶n=1, 2, ...}], or the pseudocharacter of x in X is no greater than countable. In other words, if X is a hereditary Souslin bicompactum which is a χ-space, then X is a Frechet-Urysohn space.