$\epsilon$-neighbourhoods in the Plane with a Nowhere-smooth Boundary

Jeroen S. W. Lamb, Martin Rasmussen, Kalle G. Timperi

We give an example of a planar set $E\subset {\mathbb{R}}^2$ for which the boundary $\partial E_{\epsilon }$ of its $\epsilon$-neighbourhood $E_\varepsilon = \{x \in \mathbb{R}^2…