Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 2G / i / Solution

A set is of first Baire category, or meagre, when it is a countable union of nowhere dense sets. The statement is true: a countable union of countable unions of nowhere dense sets is again a countable union of nowhere dense sets.

The relevant Baire category theorem says that a nonempty complete metric space is not meagre in itself.

Solved by gpt-5.6-sol high.