Meager set - Imported Knowlpedia Content

A meager set in a topological space $X$ is a subset $M\subseteq X$ that can be written as a countable union of nowhere dense sets.

Meager sets are also called “sets of first category.” Their complements are the residual sets; in a Baire space, meager sets are topologically “small.”

Examples

Any countable subset of $\mathbb{R}$ (with the usual topology), such as the rationals $\mathbb{Q}$ , is meager (a countable union of singleton sets, each nowhere dense).
Any nowhere dense set is meager (as a countable union of itself).