Source: wikibot/totally-bounded-space
= Totally bounded space
{wiki=Totally_bounded_space}
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 \\).