Baire space

A Baire space is a type of mathematical space used in topology, which is a branch of mathematics that studies the properties of space. In simple terms, a Baire space is a space where you can make certain meaningful distinctions between "large" sets and "small" ones. Specifically, if you take a countable collection of closed sets that are each "small" (having no interior points), their union is still "small." This concept is important in analysis and helps us understand continuity and limits in functions, providing a framework for many advanced mathematical theories.