A locally connected curve A is said to be an asymptote of the locally connected curve B when the following is true: » For any positive epsilon, there exist unbounded connected subsets (pieces of the respective curves) A^primesubseteq A and B^primesubseteq B, such that for every point in A^prime its distance to the nearest point in B^prime is lower than epsilon. In other words, as one moves along B in some direction, the distance between it and the asymptote A eventually becomes smaller than any… (More on Asymptote)