Exercise 7, § 5

A topological space $X$ is said to be non-meagre if it is not meagre relative to itself.

a) $X$ is non-meagre if and only if every countable family of dense open sets in $X$ has a non-empty intersection.

b) In a non-meagre space, the complement of every meagre set is a non-meagre subspace.