Alexandroff plank

The set $[0,\omega_1] \times [-1,1]$ with topology generated by adding in all sets of the form $U(\alpha, n) = \{(\omega_1,0)\} \cup (\alpha, \omega_1] \times (0,\frac{1}{n})$ to its usual product topology.

Defined as counterexample #88 ("Alexandroff Plank") in DOI 10.1007/978-1-4612-6290-9.