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knot exterior

纽结外部

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Mathematical Physics: Classical Mechanics 封面

《Mathematical Physics: Classical Mechanics》 · 第 11 页 · Chapter 1,Theorem 1.5 前的完整定义;exterior 保留邻域边界

Suppose that \(K\) is a knot in \(S^3\). Then \(K\) has a regular neighbourhood \(N\) that is a solid torus. […] The exterior \(X\) of \(K\) is the closure of \(S^3-N\). Thus \(X\) is a connected 3-manifold, with boundary \(\partial X\) that is a torus. This \(X\) has the same homotopy type as \(S^3-K\), \(X\cap N=\partial X=\partial N\) and \(X\cup N=S^3\).

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