Why is every one dimensional Complex Manifold paracompact?
$begingroup$
I read on the page
Why are smooth manifolds defined to be paracompact?
in one of the answers that every one dimensional complex manifold is automatically paracompact, i.e. there is no complex analogue to the real long line.
My problem: I cant find any book or paper explaining me why this should be the case. In most textbooks, a complex manifold is defined to be paracompact even if this was not necessary in this case.
So: Why is every one dimensional Complex Manifold paracompact?
complex-geometry riemann-surfaces paracompactness
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
asked Feb 20 '14 at 12:09
TomTom
23616
$endgroup$
add a comment |
$begingroup$
I read on the page
Why are smooth manifolds defined to be paracompact?
in one of the answers that every one dimensional complex manifold is automatically paracompact, i.e. there is no complex analogue to the real long line.
My problem: I cant find any book or paper explaining me why this should be the case. In most textbooks, a complex manifold is defined to be paracompact even if this was not necessary in this case.
So: Why is every one dimensional Complex Manifold paracompact?
complex-geometry riemann-surfaces paracompactness
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
asked Feb 20 '14 at 12:09
TomTom
23616
$endgroup$
2
$begingroup$
This is Radó's theorem. You can find a proof on page 186 of Forster's magnificent Lectures on Riemann Surfaces .
$endgroup$
– Georges Elencwajg
Feb 20 '14 at 13:49
$begingroup$
You are welcome, Tom.
$endgroup$
– Georges Elencwajg
Feb 25 '14 at 12:22
add a comment |
$begingroup$
I read on the page
Why are smooth manifolds defined to be paracompact?
in one of the answers that every one dimensional complex manifold is automatically paracompact, i.e. there is no complex analogue to the real long line.
My problem: I cant find any book or paper explaining me why this should be the case. In most textbooks, a complex manifold is defined to be paracompact even if this was not necessary in this case.
So: Why is every one dimensional Complex Manifold paracompact?
complex-geometry riemann-surfaces paracompactness
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
asked Feb 20 '14 at 12:09
TomTom
23616
$endgroup$
I read on the page
Why are smooth manifolds defined to be paracompact?
in one of the answers that every one dimensional complex manifold is automatically paracompact, i.e. there is no complex analogue to the real long line.
My problem: I cant find any book or paper explaining me why this should be the case. In most textbooks, a complex manifold is defined to be paracompact even if this was not necessary in this case.
So: Why is every one dimensional Complex Manifold paracompact?
complex-geometry riemann-surfaces paracompactness
complex-geometry riemann-surfaces paracompactness
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
asked Feb 20 '14 at 12:09
TomTom
23616
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
asked Feb 20 '14 at 12:09
TomTom
23616
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
edited Dec 9 '18 at 22:10
Eric Wofsey
183k13209337
183k13209337
asked Feb 20 '14 at 12:09
TomTom
23616
asked Feb 20 '14 at 12:09
TomTom
23616
asked Feb 20 '14 at 12:09
TomTom
23616
23616
2
$begingroup$
This is Radó's theorem. You can find a proof on page 186 of Forster's magnificent Lectures on Riemann Surfaces .
$endgroup$
– Georges Elencwajg
Feb 20 '14 at 13:49
$begingroup$
You are welcome, Tom.
$endgroup$
– Georges Elencwajg
Feb 25 '14 at 12:22
add a comment |
2
$begingroup$
This is Radó's theorem. You can find a proof on page 186 of Forster's magnificent Lectures on Riemann Surfaces .
$endgroup$
– Georges Elencwajg
Feb 20 '14 at 13:49
$begingroup$
You are welcome, Tom.
$endgroup$
– Georges Elencwajg
Feb 25 '14 at 12:22
2
2
$begingroup$
This is Radó's theorem. You can find a proof on page 186 of Forster's magnificent Lectures on Riemann Surfaces .
$endgroup$
– Georges Elencwajg
Feb 20 '14 at 13:49
$begingroup$
This is Radó's theorem. You can find a proof on page 186 of Forster's magnificent Lectures on Riemann Surfaces .
$endgroup$
– Georges Elencwajg
Feb 20 '14 at 13:49
$begingroup$
You are welcome, Tom.
$endgroup$
– Georges Elencwajg
Feb 25 '14 at 12:22
$begingroup$
You are welcome, Tom.
$endgroup$
– Georges Elencwajg
Feb 25 '14 at 12:22
add a comment |
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$begingroup$
This is Radó's theorem. You can find a proof on page 186 of Forster's magnificent Lectures on Riemann Surfaces .
$endgroup$
– Georges Elencwajg
Feb 20 '14 at 13:49
$begingroup$
You are welcome, Tom.
$endgroup$
– Georges Elencwajg
Feb 25 '14 at 12:22