“EquivalentStatementOfBaireCategoryTheorem”的概念、定义、习题解题方法及翻译-数学辞典

单词	EquivalentStatementOfBaireCategoryTheorem
释义	equivalent statement of Baire category theorem Let $(X,d)$ be a complete metric space. Then every subset $B\\subset X$ of first category has empty interior. Corollary: Every non empty complete metric space is of second category.
随便看	every even integer greater than 70 is the sum of two abundant numbers in more than one way EveryFilterIsContainedInAnUltrafilter every filter is contained in an ultrafilter EveryFiniteDimensionalNormedVectorSpaceIsABanachSpace every finite dimensional normed vector space is a Banach space EveryFiniteDimensionalSubspaceOfANormedSpaceIsClosed every finite dimensional subspace of a normed space is closed EveryHilbertSpaceHasAnOrthonormalBasis every Hilbert space has an orthonormal basis EveryLocallyIntegrableFunctionIsADistribution every locally integrable function is a distribution EveryMapIntoSphereWhichIsNotOntoIsNullhomotopic every map into sphere which is not onto is nullhomotopic EveryNetHasAUniversalSubnet every net has a universal subnet EveryNormedSpaceWithSchauderBasisIsSeparable every normed space with Schauder basis is separable EveryOrderedFieldWithTheLeastUpperBoundPropertyIsIsomorphicTomathbbRProofThat EveryOrderedFieldWithTheLeastUpperBoundPropertyIsIsomorphicToTheRealNumbers every ordered field with the least upper bound property is isomorphic to the real numbers every ordered field with the least upper bound property is isomorphic to ℝ, proof that EveryOrthonormalSetIsLinearlyIndependent every orthonormal set is linearly independent EveryPermutationHasACycleDecomposition every permutation has a cycle decomposition

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

equivalent statement of Baire category theorem