'nonmetrizable' originates from English, specifically the prefix 'non-' and the adjective 'metrizable', where 'non-' meant 'not' and the root 'metr-' (via 'metric') meant 'measure'.

'metrizable' developed from the adjective 'metric' (from Late Latin 'metricus' and Old French 'metrique') and the verbal/adjectival formative '-ize' + suffix '-able'; 'non-' (from Latin 'non') was later prefixed to form 'nonmetrizable'.

Initially the root 'metron' meant 'measure' in Greek; over time this produced 'metric' relating to measurement, then 'metrize/metrizable' meaning 'able to be given a metric', and finally 'nonmetrizable' came to mean 'not able to be given a metric'.