浸入
数学上，浸入是微分流形之间的可微映射，其导数处处是单射。确切而言，f : M → N是浸入，若在M中每一点p，
都是单射。（TpX表示X在点p处的切空间。另一个等价说法是f是浸入，若f的秩是常数，且等于M的维数：
以上只要求f的导数为单射，但映射f未必是单射。
一个与浸入相关的概念是嵌入。光滑嵌入是一个单射浸入f : M → N而同时为拓扑嵌入，使得M与其在N中的像微分同胚。浸入正是局部嵌入，即对M中每一点x都有一个x的邻域U ⊂ M，使得f : U → N是嵌入。相反地，局部嵌入都是浸入。
若M是紧致的，则单射浸入是一个嵌入；若M不是紧致，则未必成立。这两者的关系就如同连续双射之于同胚。
参考
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