2
$\begingroup$

Square Peg Problem (or conjecture) is so famous. See this article

Let $CS:=\{\gamma:S^1\longmapsto\mathbb{R}^2 | \;\;\text {Square Peg Problem is true}\}$ and $C=\{\Upsilon:S^1\longmapsto\mathbb{R}^2 \}$.

Is this true that $CS$ is dense in the set $C$? Is there any results in this direction?

$\endgroup$
  • 1
    $\begingroup$ Well, wikipedia says that polygons are in $CS$ and if they are not dense in $C$ in topology you are thinking about then you should definitely tell us which topology you are imposing on $C$. Actually, for dense subset of polygons it is obvious that they are in $CS$ -- start with arbitrary polygon and add small square bump on one of it sides. $\endgroup$ – Aleksei Kulikov Jun 26 '18 at 10:28

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.