# Tagged Questions

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 ...
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 ...
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 ...
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 ...
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 ...
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9392091631889343, "perplexity_flag": "head"}