Quelques propriétés des espaces $\alpha $-favorables et applications aux convexes compacts

Abstract

Let X be a topological regular space which is strongly α-favorable. If X is a continuous image of a separable metrizable space then X is a Lusin space; this gives an answer to a question of R. Haydon. If X is only Lindelöf and is separated by a countable family of continuous functions, then the measurable space (X,Ba(X)) is standard; if X is the set of the extreme points of a compact convex set K and satisfies the preceding assumptions, then K is metrizable.