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게시글 주소: https://orbi.kr/00040061713
Thm. Let $M$ and $N$ be closed $R$-orientable manifolds with dimension $m$ and $n$ respectively. If $\{\mu_x\}_{x\in M}$ and $\{\mu_y\}_{y\in N}$ are local orientations of $M$ and $N$ then
$$\{\mu_x\times\mu_y\mid x\in M, y\in N\}$$
defines a local orientation of $M\times N$ where $\otimes$ is a homology cross product. Moreover, if $[M]$ and $[N]$ are fundamental classes of $M$ and $N$ respectively, then $[M]\times [N]$ is a fundamental class of $M\times N$.
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