ИСТИНА

Theorem 1. MA(\omega_1) If $f$ is a 0-soft mapping of a space $X$ of weight $\leq\omega_1$ to the polish space $Y$ , then mapping $U_\tau(f)$ is soft. Theorem 2. MA(\omega_1) If $X$ is $AE(0)$ and $wX\leq\omega_1$, then $U_\tau(X)$ in $AE$.