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Concepts related to Baire spaces
Characterizations of Baire spaces
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5-open functions adherent point Baire Category Theorem Baire space Baire)-space cardinality category subset Characterizations of Baire closed nowhere dense closed subset complete metric space complete space contains a dense continuum hypothesis Corollary countable chain condition countable union countably infinite countably subcompact countably-Baire space d-open define dense Baire subspace dense open subset dense set dense subset dense subspace exists a nonempty feebly open finite open cover following are equivalent Hence implies intersects isolated points Let F locally finite metric Baire space metrizable Baire nonempty open set nonempty open subset nonempty set open Baire subspace open filter base open ultrafilters point finite open positive integer Proof pseudo pseudo-complete space pseudo-cover quasi-regular quasi-regular space regular filter base second category sequence of dense set of points space of second space X,& strong sense Suppose topological space Urysohn spaces weakly a-favorable Xv-category subset Zorn's lemma