On positively differentiable curves with values in normed linear spaces

Abstract

We prove a theorem that characterizes continuous normed linear space-valued curves allowing differentiable parameterizations with non-zero derivatives as those curves, all the points of which are regular (in Choquet's sense). We also state an equivalent geometric condition not involving any homeomorphisms.

This extends a theorem due to Choquet, who proved a similar result for curves with values in Euclidean spaces.

Keywords

• positively
• differentiable
• curves
• values
• normed
• linear
• spaces