Section 24: Problem 9 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
For any point there is an uncountable number of lines passing through it which do not intersect
. For any two points there is a pair of lines that do intersect each other but do not intersect the set
. So, both points are connected to the point of intersection of the lines, and, therefore, are connected.