Define a new metric d on X = (0, 1/2)^2 by d((a,b), (r,s)) = 1 if a is not equal to r Or |b - s| if a = r.
a) Show that d is a metric on X.
b) What are the compact subsets of X? Prove your statement.
This solution explains how to prove that one variable is a subset of another one. Additionally, it shows how to prove what the compact subsets are of the given variable.