Summary
This paper begins with another proof of a theorem of W. Benz [2] concerning dilations in normed linear spaces. Our proof motivates several questions which are addressed thereafter. For instance it is shown that, ifI is an open interval in ℝ,γ: I → ℝn,γ is continuously differentiable and there exista 1,...,a n ∈I such that {γ′(a 1,...,γ′(a n )} is linearly independent, then {γ(t): t ∈ I} contains a Hamel basis for ℝn over ℚ.
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