Maximal smooth atlas of an open subset $U$ of a smooth manifold $M$
$begingroup$
Let $M$ be a smooth $n$-dimensional manifold, with smooth maximal atlas $mathcal{A}:={varphi:O_a rightarrow varphi(O_a)| a in A}$. If I take an open subset $U subset M$, and endow it with the smooth atlas
$$mathcal{A}_U:={ varphi_{Ucap O_a}:Ucap O_a rightarrow varphi(U cap O_a) | a in A},$$
is $mathcal{A}_U$ then also a maximal smooth atlas for $U$ ?
differential-geometry manifolds riemannian-geometry smooth-manifolds
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
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add a comment |
$begingroup$
Let $M$ be a smooth $n$-dimensional manifold, with smooth maximal atlas $mathcal{A}:={varphi:O_a rightarrow varphi(O_a)| a in A}$. If I take an open subset $U subset M$, and endow it with the smooth atlas
$$mathcal{A}_U:={ varphi_{Ucap O_a}:Ucap O_a rightarrow varphi(U cap O_a) | a in A},$$
is $mathcal{A}_U$ then also a maximal smooth atlas for $U$ ?
differential-geometry manifolds riemannian-geometry smooth-manifolds
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
$endgroup$
add a comment |
$begingroup$
Let $M$ be a smooth $n$-dimensional manifold, with smooth maximal atlas $mathcal{A}:={varphi:O_a rightarrow varphi(O_a)| a in A}$. If I take an open subset $U subset M$, and endow it with the smooth atlas
$$mathcal{A}_U:={ varphi_{Ucap O_a}:Ucap O_a rightarrow varphi(U cap O_a) | a in A},$$
is $mathcal{A}_U$ then also a maximal smooth atlas for $U$ ?
differential-geometry manifolds riemannian-geometry smooth-manifolds
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
$endgroup$
Let $M$ be a smooth $n$-dimensional manifold, with smooth maximal atlas $mathcal{A}:={varphi:O_a rightarrow varphi(O_a)| a in A}$. If I take an open subset $U subset M$, and endow it with the smooth atlas
$$mathcal{A}_U:={ varphi_{Ucap O_a}:Ucap O_a rightarrow varphi(U cap O_a) | a in A},$$
is $mathcal{A}_U$ then also a maximal smooth atlas for $U$ ?
differential-geometry manifolds riemannian-geometry smooth-manifolds
differential-geometry manifolds riemannian-geometry smooth-manifolds
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
asked Nov 24 '18 at 16:22
vaoyvaoy
537210
537210
add a comment |
add a comment |
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