Definition:Meager Space

Definition
Let $\left({X, \vartheta}\right)$ be a topological space.

Let $A \subseteq X$.

Then $A$ is meager in $X$ iff it is the union of a countable set of subsets of $X$ which are nowhere dense in $X$.

A set which is meager in $X$ is also called of the first category in $X$.

Non-Meager
A set which is not meager is called non-meager in $X$ or of the second category in $X$.

Linguistic Note
The word meager (British English: meagre) is a somewhat old-fashioned word meaning deficient, lacking, scrawny etc.

It originates from the French maigre, meaning thin in the sense of unhealthily skinny.