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Vladimir V. Tkachuk ) E?A ?=II ANJH=?JA@ BH C

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Vladimir V. Tkachuk

A nice class extracted from

Cp

-theory

Comment.Math.Univ.Carolinae 46,3 (2005) 503-513.

Abstract: 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 Fr´echet-Urysohn and the space Cp(X) is Lindel¨of.

We prove that any Sokolov space with aGδ-diagonal has a countable network and obtain some cardinality restrictions on subsets of small pseudocharacter lying in Σ-products of cosmic spaces.

Keywords: Corson compact space, Sokolov space, extent, ω-monolithic space, Σ-products

AMS Subject Classification: 54B10, 54C05, 54D30

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