Countable box product of reals

The set $\mathbb{R}^\omega$ with the box product topology where basic open sets are of the form $\prod_{i<\omega}U_i$ for $U_i$ open in $\mathbb R$. Also known as the Boolean product.

Defined as counterexample #109 ("Box Product Topology on $\mathbb{R}^\omega$") in DOI 10.1007/978-1-4612-6290-9.