“embedding”的概念、定义、习题解题方法及翻译-数学辞典

单词

embedding

释义

embedding

In general, an embedding of X in Y is an injection f: X → Y such that the intrinsic structure of X agrees with the structure inherited extrinsically from the ambient space Y. This is commonly denoted as f: X ↪ Y.

In algebra this means that the map is an isomorphism onto its image, in topology a homeomorphism onto its image, etc. For smooth manifolds, a smooth embedding is a diffeomorphism onto its image such that the differential is injective everywhere. This means that the image will also be a smooth manifold.

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