## Mapping $\mathbb P$ onto $\mathbb Q ^\omega$

Let $\mathbb P$ denote the space of irrationals. Is there a continuous bijection (one-to-one and onto) $f:\mathbb P\to \mathbb Q ^\omega$ that maps each closed subset of $\mathbb P$ to a $G_\delta$-subset of $\mathbb Q ^\omega$? Remark 1. Suppose that $f:\mathbb P\to \mathbb Q ^\omega$ is a continuous bijection mapping closed sets to $G_{\delta}$ sets. … Read more