Definition talk:Smooth Path/Simple/Complex Plane

Could it be that condition (2) is superfluous, since $\gamma(a) = \gamma(b)$? If $\gamma$ is injective on $[a..b)$ then, for all $t$ in $[a..b)$, if $\gamma(t) = \gamma(a)\ [= \gamma(b)]$ then $t = a$, hence there is no such $t$ in $(a..b)$. In other words, for all $t \in (a..b)$ we have $\gamma(t) \ne \gamma(b)$, which is condition (2). --Plammens (talk) 18:37, 26 February 2021 (UTC)

No because $b$ is not in the interval over which the function is injective.

Where does it say $\map \gamma a = \map \gamma b$? --prime mover (talk) 20:26, 26 February 2021 (UTC)

My bad, for some reason I had in mind a closed path and not a general path. --Plammens (talk) 21:14, 26 February 2021 (UTC)