Adjective
metrisable (not comparable)
Alternative form of metrizable
;Locally metrizable/Locally metrisable: A space is locally metrizable if every point has a metrizable neighbourhood. Source: Internet
The first definition is usually taken for locally compact, countably compact, metrisable, separable, countable; the second for locally connected. Source: Internet
The last fact follows from f(X) being compact Hausdorff, and hence (since compact metrisable spaces are necessarily second countable); as well as the fact that compact Hausdorff spaces are metrisable exactly in case they are second countable. Source: Internet