On questions which are connected with Talagrand problem

We prove the following results.

If $X$ is a $α$ -favourable space, $Y$ is a regular space, in which every separable closed set is compact, and $f : X \times Y \to R$ is a separately continuous everywhere jointly discontinuous function, then there exists a subspace $Y_{0} \subseteq Y$ which is homeomorphic to $β N$ .
There exist a $α$ -favourable space $X$ , a dense in $\beta\mathbb N\setminus\mathbb N $c o u n t a b l y c o m p a c t s p a c e$ Y$ and a separately continuous everywhere jointly discontinuous function $f : X \times Y \to R$ . Besides, it was obtained some conditions equivalent to the fact that the space $C_{p} (β N ∖ N, {0, 1})$ of all continuous functions $x : β N ∖ N \to {0, 1}$ with the topology of point-wise convergence is a Baire space.

We prove the following results.

If $X$ is a $α$ -favourable space, $Y$ is a regular space, in which every separable closed set is compact, and $f : X \times Y \to R$ is a separately continuous everywhere jointly discontinuous function, then there exists a subspace $Y_{0} \subseteq Y$ which is homeomorphic to $β N$ .
There exist a $α$ -favourable space $X$ , a dense in $\beta\mathbb N\setminus\mathbb N $c o u n t a b l y c o m p a c t s p a c e$ Y$ and a separately continuous everywhere jointly discontinuous function $f : X \times Y \to R$ . Besides, it was obtained some conditions equivalent to the fact that the space $C_{p} (β N ∖ N, {0, 1})$ of all continuous functions $x : β N ∖ N \to {0, 1}$ with the topology of point-wise convergence is a Baire space.

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