Tagged Questions
2
votes
1answer
50 views
Fundamental group of the following disc
What is the fundamental group of the following space in $\mathbf C^n$?
This is the topological space given by $$\{(x_1,\ldots,x_n)\in \mathbf C^n-\{0\} : \vert x_1\vert < 1, \ldots, \vert x_n\vert ...
4
votes
2answers
126 views
Why is $x^2$ +$ y^2$ = 1, where $x$ and $ y$ are complex numbers, a sphere?
I've heard $x^2 + y^2$ = 1, where $x$, $y$ are complex numbers, is supposed to be a sphere with two points removed, or also a cylinder. The problem is I've been trying to wrap my head around this for ...
0
votes
1answer
159 views
A consequence of Runge's theorem
I'd like to have a reference for the proof of the following fact of complex analysis. I think it follows from Runge's theorem, but I don't know how to prove it.
Fact. Let $U \subseteq V \subseteq ...
1
vote
1answer
69 views
The $0$-section of sheaf
I ran into a problem with a defintion in Complex Analysis as follows:
A sheaf $\mathscr S$ over a paracompact Hausdorff space $X$ with a map $f: \mathscr S \to X$ such that
(1) $f$ is surjective and ...
2
votes
0answers
97 views
Definition of a complex analytic space
A complex analytic space is a topological space (say, Hausdorff and second countable) such that each point has an open neighborhood homeomorphic to some zero set $V(f_1,\ldots,f_k)$ of finitely many ...
