Property of Baire

A subset ${\displaystyle A}$ of a topological space ${\displaystyle X}$ has the property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is, if there is an open set ${\displaystyle U\subseteq X}$ such that ${\displaystyle A{\mathbin {\Delta }}U}$ is meager (where Δ denotes the symmetric difference).

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