What is a punctured disk? I am reading Voisin Book (Hodge Theory and Complex Algebraic Geometry) and I found this term and I would like to know what is it. Thank you!!
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1$\begingroup$ It is what you get when you drop an $\epsilon$ ball on a thorny mathematics problem. $\endgroup$– copper.hatFeb 15, 2020 at 22:20
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1 Answer
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It just means a disk minus a point (or the disk minus the point). Most often this means $\{(x,y)\in \Bbb R^2:0<x^2+y^2\le 1\}$, but occasionally people mean the open disk $\{(x,y)\in \Bbb R^2:0<x^2+y^2<1\}$
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2$\begingroup$ Just one minor addition: in the context of complex geometry (as is mentioned in the question), this is usually viewed as a subset of $\Bbb C$ rather than just $\Bbb R^2$. $\endgroup$– KReiserFeb 15, 2020 at 22:09
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$\begingroup$ True. Since this is tagged algebraic topology, if it wasn't clear to OP, the two are topologically the same. $\endgroup$– panciniFeb 15, 2020 at 22:16