  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 closed polygons, $\mathcal K_P$ of polygonal
knots, and $\mathcal K_T$ of tame knots. We prove that all the hyperspaces are
strongly locally contractible, arcwise connected, infinite-dimensional Cantor
manifolds, and $\mathcal S(\mathbb R^2)$ and $\mathcal K_T$ are strongly
infinite-dimensional Cantor manifolds. Moreover, $\mathcal S_P(\mathbb R^2)$
and $\mathcal K_P$ are $\sigma$-compact, strongly countable-dimensional
absolute neighborhood retracts.
