A subset E of the metric space (X,ρ) is totally bounded if for all ε>0, there exists a finite set xii=1n of points in X such that E⊆i=1⋃nB(xi,ε), where B(xi,ε)=x∈X∣ρ(xi,x)<ε. That is, for every ε>0, E can be covered by a finite set of balls of radius ε.
Wikidata ID: Q1362228