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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    $\begingroup$ It is what you get when you drop an $\epsilon$ ball on a thorny mathematics problem. $\endgroup$
    – copper.hat
    Commented Feb 15, 2020 at 22:20

1 Answer 1


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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    $\begingroup$ 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 $\Bbb R^2$. $\endgroup$
    – KReiser
    Commented Feb 15, 2020 at 22:09
  • $\begingroup$ True. Since this is tagged algebraic topology, if it wasn't clear to OP, the two are topologically the same. $\endgroup$
    – pancini
    Commented Feb 15, 2020 at 22:16

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