The projectively Hurewicz property is t-invariant

Abstract

A space $X$ is projectively Hurewicz provided every separable metrizable continuous image of $X$ is Hurewicz. In this paper we prove that the projectively Hurewicz property is $t$-invariant, i.e., if $C_p(X)$ is homeomorphic to $C_p(Y)$ and $X$ is projectively Hurewicz, then $Y$ is projectively Hurewicz, too.