non-metrizable
|non-me-tri-za-ble|
🇺🇸
/ˌnɑnˈmɛtrɪzəbəl/
🇬🇧
/ˌnɒnˈmɛtrɪzəb(ə)l/
not able to be given a metric
Etymology
'non-metrizable' originates from English, specifically formed by the prefix 'non-' and the adjective 'metrizable', where 'non-' meant 'not' and 'metrizable' meant 'able to be given a metric.'
'Metrizable' is built from 'metric' (from Greek 'metron' meaning 'measure') plus the verb-forming suffixes '-ize' and the adjective suffix '-able'; 'non-' was then prefixed in modern English to indicate negation, yielding 'non-metrizable'.
Initially the elements 'metric' and related forms meant 'measure' or 'related to measure'; by suffixation they came to mean 'able to be given a metric', and the prefixed form 'non-metrizable' simply denotes the negation 'not able to be given a metric' (the basic meaning has been stable in technical usage).
Meanings by Part of Speech
Noun 1
the property or condition of being non-metrizable (i.e., the fact that a space cannot be given a metric inducing its topology)
The non-metrizable nature of the space follows from its lack of a countable base.
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Adjective 1
(of a topological space) not metrizable; not having a topology induced by any metric
The long line is a classical example of a non-metrizable manifold.
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Last updated: 2025/11/23 12:04