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complete metric space
[/kəmˈpliːt ˈmetrɪk speɪs/]
noun
pl: complete metric spaces
espaço métrico completo
1.
A metric space in which every Cauchy sequence converges to a point within the space
The real numbers form a complete metric space under the standard distance metric.
Os números reais formam um espaço métrico completo sob a métrica de distância padrão.
2.
A topological space where no point is missing from any sequence that should converge
In a complete metric space, we can guarantee the existence of limits for Cauchy sequences.
Em um espaço métrico completo, podemos garantir a existência de limites para sequências de Cauchy.
Synonyms
Banach space (when equipped with a norm)
complete space
Antonyms
incomplete metric space
non-complete metric space
Regional Variations
General Brazilian
espaço métrico completo
Standard term used in mathematics education and research
Portugal
espaço métrico completo
Standard term used in Portuguese universities and mathematical texts
Related Idioms & Phrases
Cauchy sequence in a complete metric space
completeness of a metric space
complete normed vector space
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