On the perfect matching of disjoint compact sets by noncrossing line segments in R~n

摘要

Let V be a family of even disjoint line segments in R~n of f-equal width for a direction f ∈(R~n)~*(n ≥ 2), or even disjoint curve segments in R~n of f_n-equal width, where f_n is the normal direction for bases (n ≥ 2), or even disjoint twisted triangular prisms in R~3 of f_3-equal width. We prove that V has a perfect matching by open disjoint line segments in the complementary domain of the union of all the elements of V.