Analysis/Topology: Bounded and Totally Bounded Sets

Definitions Bounded set: Let <M,ρ> be a metric space. We say that the subset A of M is bounded if there exists a positive number L such that ρ(x,y)≤L  (x,y∈A) (Wikipedia) Diameter of a set: If A is bounded, we define diameter of A (denoted by diam A) as diam A=  ρ(x,y). If A is not…