Lecture 19 (Topology)

A metric on X is a function d: X × X → R required to satisfy which three conditions?

1. A.Nonnegativity with d(x,y)=0 iff x=y; symmetry; the triangle inequality
2. B.Nonnegativity; linearity; the parallelogram law
3. C.Positivity; continuity; the Cauchy–Schwarz inequality
4. D.Nonnegativity; symmetry; preservation of open sets