baire space in a sentence

Examples

1. However there are separable metric spaces where neither player has a winning strategy, so there are Baire spaces that are not Choquet spaces.
2. Note that elements of the Cantor space can be identified with sets of integers and elements of the Baire space with functions from integers to integers.
3. A point in Baire space is in an open set if and only if its path goes through one of the nodes in its determining union.
4. By "'BCT2 "', every finite-dimensional Hausdorff manifold is a Baire space, since it is locally compact and Hausdorff.
5. A parallel definition is used to define the arithmetical hierarchy on finite Cartesian powers of Baire space or Cantor space, using formulas with several free variables.
6. A topological space " X " is a Baire space if and only if every comeager subset of " X " is dense.
7. "' BCT2 "'shows that every manifold is a Baire space, even if it is not paracompact, and hence not metrizable.
8. In set theory, the "'Baire space "'is the set of all infinite sequences of natural numbers with a certain topology.
9. Thus a basic open set in the Baire space is the set of all infinite sequences of natural numbers extending a common finite initial segment & tau;.
10. Wadge had analyzed the structure of the Wadge hierarchy for Baire space with games by 1972, but published these results only much later in his PhD thesis.