Section 23: Problem 6 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
Let
. Show that if
is a connected subspace of
that intersects both
and
, then C intersects
.
If
does not intersect the boundary, then
and
is a separation of
.