What are the application of result "Every compact metric space is separable"?
I wanted to do some exrecise problem which uses the result Every compact metric space is separable so that I can understand the result upto the fullest.
Please suggest some exercise problems...
Thank you
The result has as immediate consequence that a compact non-separable space is not metrisable, so e.g. $[0,1] \times [0,1]$ in the order topology induced by the lexicographic order (the lexicographically ordered square) is not metrisable.