Is any second category space a Baire space?

Answer 1

Yes, any second category space is a Baire space. A topological space is considered to be of second category if it cannot be expressed as a countable union of nowhere dense sets. Baire spaces are defined by the property that the intersection of countably many dense open sets is dense. Therefore, since second category spaces avoid being decomposed into countable unions of nowhere dense sets, they satisfy the conditions to be classified as Baire spaces.