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I was wondering if central projections between planes are continuous functions.

By central projection I mean the following: let $\Gamma$ and $\Omega$ be planes in $\mathbb{R}^3$ and let $p$ be a point of neither. A central projection $f$ maps a point $a$ of $\Gamma$ to a point $b$ of $\Omega$ if the line $\overline{ap}$ meets $\Omega$ at $b$.

NamelessCuriosity
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  • Ask yourself: "if I limit the movement of $a$ to small enough of a range, am I guaranteed to be able to keep the movement of $b$ small as well"? If this is true, whatever function $b$ is of $a$ is continuous. If it is false (i.e., no matter how small you limit the movement of $a, b$ may take a big jump), then the function is discontinuous. For this particular function, it is pretty simple to show that it is continuous. – Paul Sinclair Aug 30 '19 at 02:33
  • Note that $f$ is not actually defined on every point of $\Gamma$ if $\Gamma$ and $\Omega$ are not parallel. But $f$ is continuous wherever it is defined. – Magma Aug 30 '19 at 20:21

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