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Totally bounded space

 Home Mathematics Fields of mathematics Geometry Fields of geometry Metric geometry
 0 By others on same topic  0 Discussions  1970-01-01  See my version
In mathematics, particularly in the field of functional analysis and metric spaces, a subset \( S \) of a metric space \( (X, d) \) is said to be **totally bounded** if, for every \( \epsilon > 0 \), there exists a finite cover of \( S \) by open balls of radius \( \epsilon \).

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