Meagre set

In the context of mathematical analysis and topology, a **meagre set** (also known as a **first category set**) is a set that can be expressed as a countable union of nowhere dense sets. A set \( A \) is said to be nowhere dense in a topological space \( X \) if the interior of its closure is empty; that is, there are no open sets in \( X \) that contain any points of \( A \) in a non-empty way.