Continuity of scalar-fields characterized by smooth paths fulfilling $\|\bs(t)\|\|\bs'(t)\| < +\infty$

Sigurdur F. Hafstein

A function $f$ from a subset of ${\mathbb{R}}^n$ to $\mathbb{R}$ is continuous at the origin, if and only if $\lim_{t\to 0+} f(\bs(t))=f(\bnull)$ for all continuous paths $\bs$ with $\lim_{t\to 0+}…