Definition:Meager Space/Non-Meager

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$.

$A$ is non-meager in $T$ it can not be constructed as a countable union of subsets of $S$ which are nowhere dense in $T$.

That is, $A$ is non-meager in $T$ it is not meager in $T$.

Also known as
A subset which is non-meager in $T$ is also referred to as of the second category in $T$.