Charles University in Prague, Faculty of Mathematics and Physics
Abstract
summary:We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, ω-stable and ω-monolithic. It is also established that any Sokolov compact space X is Fréchet-Urysohn and the space Cp(X) is Lindelöf. We prove that any Sokolov space with a Gδ-diagonal has a countable network and obtain some cardinality restrictions on subsets of small pseudocharacter lying in Σ-products of cosmic spaces