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单词 TopologicalInvariant
释义

topological invariant


A topological invariantPlanetmathPlanetmath of a space X is a property that depends only on the topologyMathworldPlanetmathPlanetmath of the space, i.e. it is shared by any topological space homeomorphic to X. Common examples include compactness (http://planetmath.org/CompactPlanetmathPlanetmath), connectedness (http://planetmath.org/ConnectedSpace), Hausdorffness (http://planetmath.org/T2Space), Euler characteristicMathworldPlanetmath, orientability (http://planetmath.org/Orientation2), dimensionMathworldPlanetmath (http://planetmath.org/InvarianceOfDimension), and like homology, homotopy groupsMathworldPlanetmath, and K-theory.

Properties of a space depending on an extra structureMathworldPlanetmath such as a metric (i.e. volume, curvature, symplectic invariants) typically are not topological invariants, though sometimes there are useful interpretationsMathworldPlanetmath of topological invariants which seem to depend on extra information like a metric (for example, the Gauss-Bonnet theorem).

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更新时间:2025/5/4 22:50:58