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## Homework Statement

Let γ : I → R

^{n}be a regular smooth curve. Show that the map γ is locally injective, that is for all t0 ∈ I there is some ε > 0 so that γ is injective when restricted to (t0 − ε , t0 + ε ) ∩ I.

## Homework Equations

## The Attempt at a Solution

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So I know a function (or a mapping) is injective when:

- {{∀a,b ∈ X}, ƒ(a) = ƒ(b) → a = b

And I get the concept here: We have an interval I and some regular smooth curve γ and when we restrict our interval to one point (t0) ± a very small number (ε) we can get a domain in which every element of the codomain is at most the image of one of the elements of the domain.

I imagine perhaps the notions of regularity and smoothness help in arguing the local injectivity of γ here but I'm just not seeing it and any help getting started on how to mathematically argue the local injectivity would be extremely appreciated!