# Compact subsets

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.

https://brainmass.com/math/geometry-and-topology/compact-subsets-364539

#### Solution Summary

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.

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