| 11. | The product topology used to define the Baire space can be described more concretely in terms of trees.
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| 12. | The representation of the Baire space as paths through a tree also gives a characterization of closed sets.
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| 13. | Conventionally, Baire space does not refer to this topology; it only refers to the product topology.
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| 14. | Therefore " R " is the complement of a subset of first category in a Baire space.
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| 15. | A "'Baire space "'is a topological space in which the interior has empty interior.
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| 16. | By definition of a Baire space, such sets ( called " residual sets " ) are dense.
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| 17. | The "'Wadge order "'is the preorder or quasiorder on the subsets of Baire space.
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| 18. | The precise definition of a Baire space has undergone slight changes throughout history, mostly due to prevailing needs and viewpoints.
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| 19. | Note that we can also define the arithmetic hierarchy of subsets of the Cantor and Baire spaces relative to some set of integers.
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| 20. | The irrationals are a Baire space in the order topology, but rationals aren't, even though both are densely ordered.
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