Lebesgue measurability of separately continuous functions and separability

2015/12/23 by V. V. Mykhaylyuk, Mykhaylyuk, V. V.
Mathematics · #FOS: Mathematics #General Topology (math.GN) #math.GN

paper · pdf · doi:10.48550/arxiv.1512.07477

arxiv created 2015/12/23 · arxiv updated 2015/12/29

Abstract

It is studied a connection between the separability and the countable chain condition of spaces with the L-property (a topological space X has the L-property if for every topological space Y, separately continuous function f:X× Y→\mathbb R and open set I⊆ \mathbb R the set f^-1(I) is a F_σ-set). We show that every completely regular Baire space with the L-property and the countable chain condition is separable and construct a nonseparable completely regular space with the L-property and the countable chain condition. This gives a negative answer to a question of M.~Burke.

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