A path $c:[a,b]→R$ is non singular if $c'(t)≠0$ for all $a≤t≤b$. This is the definition which was taught.However I am not sure if $c'(t)$ needs to be finite in the definition. Any help is appreciated.
2026-04-09 07:52:11.1775721131
Definition of non-singular curve
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A path is a continuous function, right? But if for some $\tau<\infty$ $$\lim_{t\to\tau} c'(t) = \infty,$$ it fails to be continuous.