\b[True.] If a nonempty countable complete metric space had no isolated point, every singleton would be closed and nowhere dense. Their countable union would be the whole space, contradicting the <Baire category theorem>. This is the basic <isolated points in a countable complete metric space> argument.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 2G / v / Solution

 Solution (source code)