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Metrization of the Uniform Space and Effective Convergence
Author(s) -
Yasugi Mariko,
Tsujii Yoshiki,
Mori Takakazu
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200210)48:1+<123::aid-malq123>3.0.co;2-w
Subject(s) - mathematics , convergence (economics) , space (punctuation) , pure mathematics , metrization theorem , mathematical analysis , computer science , economics , economic growth , operating system , separable space
The subject of the present article is the following fact. Consider an effective uniform space. A generally constructed metric from the uniformity has the property that a sequence from the space effectively converges with respect to the uniform topology if and only if it does with respect to the induced metric. This can be shown without assuming the computability of the metric.