from Wiktionary, Creative Commons Attribution/Share-Alike License
- adj. measurable, quantifiable
- adj. Of a set that is a topological space for which a metric exists that will induce a topology.
Sorry, no etymologies found.
But the Zariski topology is not metrizable … is a surjection of sheaves (exercise!), yet the map on global sections is not surjective.
Because of the above argument, mathematicians who work on metrizable spaces don't worry very much about the distinction between vanishing on a closed set and in the neighborhood of a closed set.