ИСТИНА

\section{Main result} \begin{theorem} \MA/ Let $X$ be a space such that the finite powers of $X$ containing no free sequences of length $\omega_1$. Then, for $Y\subset C_p(X)$, the following conditions are equivalent: \begin{enumerate} \item[(1)] $Y$ contains no uncountable discrete subspaces; \item[(2)] $Y$ is hereditarily Lindel\"of; \item[(3)] $Y$ is hereditarily separable. \end{enumerate} \end{theorem}