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.