“Closure”的概念、定义、习题解题方法及翻译-数学辞典

单词	Closure
释义	closure The closure $\\overline{A}$ of a subset $A$ of a topological space $X$ is the intersection of all closed sets containing $A$ . Equivalently, $\\overline{A}$ consists of $A$ together with all limit points of $A$ in $X$ or equivalently $x\\in\\overline{A}$ if and only if every neighborhood of $x$ intersects $A$ . Sometimes the notation $\\operatorname{cl}(A)$ is used. If it is not clear, which topological space is used, one writes $\\overline{A}^{X}$ . Note that if $Y$ is a subspace of $X$ , then $\\overline{A}^{X}$ may not be the same as $\\overline{A}^{Y}$ . For example, if $X=\\mathbb{R}$ , $Y=(0,1)$ and $A=(0,1)$ , then $\\overline{A}^{X}=[0,1]$ while $\\overline{A}^{Y}=(0,1)$ .
随便看	Classical well-orderings ClassificationOfComplexNumbers classification of complex numbers ClassificationOfCoveringSpaces classification of covering spaces ClassificationOfFinitedimensionalRepresentationsOfSemisimpleLieAlgebras classification of finite-dimensional representations of semi-simple Lie algebras ClassificationOfHilbertSpaces classification of Hilbert spaces ClassificationOfIndecomposableRootSystems classification of indecomposable root systems ClassificationOfPlatonicSolids classification of Platonic solids ClassificationOfSemisimpleGroups classification of semisimple groups ClassificationOfSeparableHilbertSpaces classification of separable Hilbert spaces ClassificationOfTopologicalPropertiesAccordingToBehaviourUnderMapping classification of topological properties according to behaviour under mapping ClassNumberDivisibilityInCyclicExtensions class number divisibility in cyclic extensions ClassNumberDivisibilityInExtensions class number divisibility in extensions ClassNumberDivisibilityInPextensions class number divisibility in p-extensions

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。

closure