I am reading a paper (Paper 1: https://ideas.repec.org/p/cwl/cwldpp/76.html, that cites another paper ( Paper 2) for its proof. Paper 1, page 1, line 10 says : Consider the topological image G of a 2-dimensional convex set and 3 families of curves in that set such that a) exactly one curve of each family goes through a point of G and b)two curves of different families have at most one common point.
I want to know if condition (a) means that exactly one curve of each family goes through every point of G, or if there can be points in G where no curve passes.
I tried to read Paper 2 to get a better idea, but it is written in German, a language I am unable to understand. Any help will be appreciated.
From what I understand, this problem is related to given 3 families of curves in a plane when is there a transformation that carries it to 3 families of parallel straight lines. The author of paper 1 calls it as Thomsen Blaschke condition, and a google search on the condition did not help me.
