Mixing
Can 2 manifolds neighbor each other
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I understand the definition of a set being a neighborhood of a point with a disk around it. But can 2 manifolds have elements in common where if m and n are manifolds of the same dimensions, there exists an element x in both m and n making m and n neighborhoods. (They are also open sets and smooth compact manifolds)
general-topology differential-geometry general-relativity
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
asked Jan 22 at 17:54
bgunerbguner
11
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add a comment |
$begingroup$
I understand the definition of a set being a neighborhood of a point with a disk around it. But can 2 manifolds have elements in common where if m and n are manifolds of the same dimensions, there exists an element x in both m and n making m and n neighborhoods. (They are also open sets and smooth compact manifolds)
general-topology differential-geometry general-relativity
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
asked Jan 22 at 17:54
bgunerbguner
11
$endgroup$
1
$begingroup$
“Neighborhood” is always used in the context of some space, here a topological space or a manifold. So “are both $M$ and $N$ neighborhoods of $x$?” is not a well-posed question. If you say “I undersand the definition of […] a neighborhood” – what's the definition you know? The details may be important.
$endgroup$
– Luke
Jan 22 at 20:00
add a comment |
$begingroup$
I understand the definition of a set being a neighborhood of a point with a disk around it. But can 2 manifolds have elements in common where if m and n are manifolds of the same dimensions, there exists an element x in both m and n making m and n neighborhoods. (They are also open sets and smooth compact manifolds)
general-topology differential-geometry general-relativity
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
asked Jan 22 at 17:54
bgunerbguner
11
$endgroup$
I understand the definition of a set being a neighborhood of a point with a disk around it. But can 2 manifolds have elements in common where if m and n are manifolds of the same dimensions, there exists an element x in both m and n making m and n neighborhoods. (They are also open sets and smooth compact manifolds)
general-topology differential-geometry general-relativity
general-topology differential-geometry general-relativity
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
asked Jan 22 at 17:54
bgunerbguner
11
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
asked Jan 22 at 17:54
bgunerbguner
11
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
edited Jan 22 at 21:29
Andrés E. Caicedo
65.7k8160250
65.7k8160250
asked Jan 22 at 17:54
bgunerbguner
11
asked Jan 22 at 17:54
bgunerbguner
11
asked Jan 22 at 17:54
bgunerbguner
11
11
1
$begingroup$
“Neighborhood” is always used in the context of some space, here a topological space or a manifold. So “are both $M$ and $N$ neighborhoods of $x$?” is not a well-posed question. If you say “I undersand the definition of […] a neighborhood” – what's the definition you know? The details may be important.
$endgroup$
– Luke
Jan 22 at 20:00
add a comment |
1
$begingroup$
“Neighborhood” is always used in the context of some space, here a topological space or a manifold. So “are both $M$ and $N$ neighborhoods of $x$?” is not a well-posed question. If you say “I undersand the definition of […] a neighborhood” – what's the definition you know? The details may be important.
$endgroup$
– Luke
Jan 22 at 20:00
1
1
$begingroup$
“Neighborhood” is always used in the context of some space, here a topological space or a manifold. So “are both $M$ and $N$ neighborhoods of $x$?” is not a well-posed question. If you say “I undersand the definition of […] a neighborhood” – what's the definition you know? The details may be important.
$endgroup$
– Luke
Jan 22 at 20:00
$begingroup$
“Neighborhood” is always used in the context of some space, here a topological space or a manifold. So “are both $M$ and $N$ neighborhoods of $x$?” is not a well-posed question. If you say “I undersand the definition of […] a neighborhood” – what's the definition you know? The details may be important.
$endgroup$
– Luke
Jan 22 at 20:00
add a comment |
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1
$begingroup$
“Neighborhood” is always used in the context of some space, here a topological space or a manifold. So “are both $M$ and $N$ neighborhoods of $x$?” is not a well-posed question. If you say “I undersand the definition of […] a neighborhood” – what's the definition you know? The details may be important.
$endgroup$
– Luke
Jan 22 at 20:00