On compactness and connectedness of the paratingent

In this note we shall prove that for a continuous function $\phi :\mathrm{\Delta }\to {\mathbb{R}}^n$, where $\mathrm{\Delta }\subset \mathbb{R}$,  the paratingent of $\phi$ at $a\in \mathrm{\Delta }$ is a non-empty and compact set in ${\mathbb{R}}^n$ if and only if $\phi$ satisfies Lipschitz condition in a neighbourhood of $a$. Moreover, in this case the paratingent is a connected set.