Metric Spaces
A Best Approximation Exists
Say you have a compact subset of the metric space. For every function value in the metric space, there's a particular point of the compact subset where the distance from that point to each function value is the smallest such distance. We write
∀a,b ∃a∗ :d(a∗,b)≤d(a,b)where a,a∗∈A,b∈B,A⊆B Operator Continuity
Normed Vector Spaces
A Best Approximation Exists
Norms Have an Ordering
Convex Balls
Unique Approximations
Operator Continuity