On hyperspaces of knots and planar simple closed curves

Paweł Krupski, Krzysztof Omiljanowski

We consider the Vietoris hyperspaces $\mathcal{S}({\mathbb{R}}^n)$ of simple closed curves in ${\mathbb{R}}^n$, $n=2,3$, and their subspaces ${\mathcal{S}}_P({\mathbb{R}}^2)$ of planar simple c…