Def 21.1 𝑆⊂𝑋 is totally bounded if (∀𝜀>0)(∃𝑚)(∃𝑥1,𝑥2,…,𝑥𝑚∈𝑋)𝑆⊂⋃𝑚𝛼=1𝐵𝜀(𝑥𝛼) where 𝐵𝜀 is Delta-ball. Thm 21.1 totally bounded ⟹ bounded