The Baire category theorem and cardinals of countable cofinality
Copyright policy )The Baire category theorem and cardinals of countable cofinality
AbstractLet κB be the least cardinal for which the Baire category theorem fails for the real line R. Thus κB is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κB cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2ω1 be ℵω. Similar questions are considered for the ideal of measure zero sets, other ω1, saturated ideals, and the ideal of zero-dimensional subsets of Rω1.
- University of Wisconsin–Oshkosh United States
- The University of Texas at Austin United States
Measures and integrals in product spaces, meager sets, Consistency and independence results in general topology, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, ideal of measure zero sets, real line, Baire category, countable cofinality
Measures and integrals in product spaces, meager sets, Consistency and independence results in general topology, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, ideal of measure zero sets, real line, Baire category, countable cofinality
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