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2.1: Manifolds A manifold is, roughly, a set in which the vicinity of every point “looks like” $\mathbb{R}^n$.
An open set is defined as a set which can be expressed as a union of open balls.
An $n$-dimensional $C^\infty$ manifold is a set $M$ and a set of open subsets ${O_\alpha}$ of $M$ satisfying
Each $p\in M$ belongs to some $O_\alpha$, i.e. ${O_\alpha}$ is an open…
2.1: Manifolds A manifold is, roughly, a set in which the vicinity of every point “looks like” $\mathbb{R}^n$.
An open set is defined as a set which can be expressed as a union of open balls.
An $n$-dimensional $C^\infty$ manifold is a set $M$ and a set of open subsets ${O_\alpha}$ of $M$ satisfying
Each $p\in M$ belongs to some $O_\alpha$, i.e. ${O_\alpha}$ is an open cover of $M$. For each $\alpha$, there is a bijection $\psi_\alpha:O_\alpha\to U_\alpha$ with $U_\alpha\subset\mathbb{R}^n$ open.Read on /journal/gr/wald-2/ ↗
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