Let $X$ be the $n$-dimensional unit sphere $S^{n}=left{x in mathbb{R}^{n+1}:|x|=1 ight}$ with antipodal points identified, and let
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Let $X$ be the $n$-dimensional unit sphere $S^{n}=\left\{x \in \mathbb{R}^{n+1}:|x|=1\right\}$ with antipodal points identified, and let $A$ be the $(n+1)$-dimensional real vector space without the point at the origin: $A=\mathbb{R}^{n+1} \backslash\{0\}$. Define an equivalence relation $\sim$ among elements of $A$, such that $X$ can be identified with the quotient space of $A$ with respect to $\sim$, i.e., $X=A / \sim$.
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Mathematical Methods For Physics An Introduction To Group Theory Topology And Geometry
ISBN: 9781107191136
1st Edition
Authors: Esko Keski Vakkuri, Claus Montonen, Marco Panero
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