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拓扑流形
拓樸空間 来自维基百科,自由的百科全书
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在数学中,拓扑流形( topological manifold )是一个“局部上看起来像是 ”的拓朴空间,是微分几何的主要研究对象。所有其他类型的流形( manifolds )都是带有额结构的拓扑流形。例如可微流形是一个带有额外的“微分结构”的拓扑流形;而光滑流形则要求这个“微分结构”要是无穷可微的。
形式定义
一个 维拓扑流形(或简称流形)是一个拓扑空间 ,满足以下性质[1]:
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范例
范例
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- Projective spaces over the reals, complexes, or quaternions are compact manifolds.
- Real projective space RPn is a n-dimensional manifold.
- Complex projective space CPn is a 2n-dimensional manifold.
- Quaternionic projective space HPn is a 4n-dimensional manifold.
- Manifolds related to projective space include Grassmannians, flag manifolds, and Stiefel manifolds.
- Differentiable manifolds are a class of topological manifolds equipped with a differential structure.
- Lens spaces are a class of differentiable manifolds that are quotients of odd-dimensional spheres.
- Lie groups are a class of differentiable manifolds equipped with a compatible group structure.
- The E8 manifold is a topological manifold which cannot be given a differentiable structure.
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参考文献
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