I'm getting confused by the following definition and examples:
A Baire space is a topological space in which any meagre set has dense complement, where a set is meagre or of first Baire category if it is a countable union of subsets which are nowhere dense in the space. A set is nowhere dense if its closure has empty interior.
The real numbers, with the usual topology, is a Baire space. The rational numbers, with the usual topology, is not a Baire space.
Could anyone show me how the two examples could be verified using the definitions? I'm having troubles seeing the properties of sets in the two spaces. Thanks.