Double (manifold)

In the subject of manifold theory in mathematics, if ${\displaystyle M}$ is a manifold with boundary, its double is obtained by gluing two copies of ${\displaystyle M}$ together along their common boundary. Precisely, the double is ${\displaystyle M\times \{0,1\}/\sim }$ where ${\displaystyle (x,0)\sim (x,1)}$ for all ${\displaystyle x\in \partial M}$.

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