EDB — 1PB

[1PB]Let \((X,d)\) be a metric space. Let \(I=[a,b]⊆ {\mathbb {R}}\) be a closed and bounded interval. Let \(𝛾:I\to X\) be a parametric curve.

• If \(𝛾(a)=𝛾(b)\) we will say that the curve is closed;

• we also say that the curve is simple and closed if \(𝛾(a)=𝛾(b)\) and \(𝛾\) is injective when restricted to \([a,b)\).  ¹

• If \(X={\mathbb {R}}^ n\) and \(𝛾\) is class \(C^ 1\) and is closed, it is further assumed that \(𝛾'(a)=𝛾'(b)\).