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Large class of curves which only intersect each other finitely many times

I am trying to find a large subset of piecewise-differentiable plane curves of finite length (subsets of $\mathbb{R}^2$) with the following property: For any pair $\gamma_1, \gamma_2$ of curves in … I have attempted to prove that this is the case for this set of curves: Piecewise-smooth curves (finite length) in which each piecewise component is either a straight line segment or a curve whose …
Joe Previdi's user avatar