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    Unit disk - Wikipedia

    In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: $${\displaystyle D_{1}(P)=\{Q:\vert P-Q\vert <1\}.\,}$$The closed unit disk around P is the set of points whose distance from P is less than or equal to one: See more

    The function
    $${\displaystyle f(z)={\frac {z}{1-|z|^{2}}}}$$
    is an example of a real analytic and bijective function … See more

    The open unit disk forms the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to … See more

    Overview image

    One also considers unit disks with respect to other metrics. For instance, with the taxicab metric and the Chebyshev metric disks look like … See more

     
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  6. 2.2: Open Disks, Open Deleted Disks, and Open …

    WEBMay 3, 2023 · Definition: Open Disk. The open disk of radius \(r\) around \(z_0\) is the set of points \(z\) with \(|z - z_0| < r\), i.e. all points within distance \(r\) of \(z_0\). The open deleted disk of radius \(r\) around …

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