EDB — 1NV

[1NV] Let \(I⊆ ℝ\) be an interval.

• A continuous function \(𝛾:I→ X\) is called parametric curve, or more simply in the following curve.

• If \(𝛾\) is injective, the curve is said to be simple.

• If \(𝛾\) is a homeomorphism onto its image, the curve is said to be embedded.

• If \(X=ℝ^ n\) and \(𝛾\) is of class \(C^ 1\) and \(𝛾'(t)≠ 0\) for every \(t∈ I\), then \(𝛾\) is called an immersed curve or regular curve.

We will call support or trace the image \(𝛾(I)\) of a curve.

The term arc is also used as a synonym for curve; ¹ this term is mainly used when the curve is not (necessarily) closed.