A Baire space is a topological space 
in which each subset of 
of the first category has
an empty interior. A topological
space which is homeomorphic to a complete
metric space is a Baire space.
In descriptive set theory, the name Baire space also denotes the particular topological space 
with the product
topology, where each factor 
has the discrete topology.
Its points are infinite sequences
of natural numbers. This space is homeomorphic
to the irrational numbers with their usual relative topology. It is a Baire space in the category
sense, but that property does not characterize this particular space (Kechris 1995).
