“manifold”的概念、定义、习题解题方法及翻译-数学辞典

单词

manifold

释义

manifold

Curves are 1‐dimensional manifolds and surfaces are 2-dimensional manifolds. Formally an n-dimensional manifold is a Hausdorff topological space X in which every point has a neighbourhood which is homeomorphic to n-dimensional Euclidean space. Note that the double cone x2 + y2 = z2 is not a manifold as no Euclidean neighbourhood of the origin exists.

The above defines what a topological manifold is, but manifolds can have further smooth or metric structure. See Classification Theorem for Surfaces, orientability, transition map, Riemann surface, Riemannian manifold.

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数学辞典收录了4151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。