Section 23: Problem 1 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
and
be two topologies on
. If
, what does connectedness of
in one topology imply about connectedness in the other?
If
is disconnected then there is a separation in the topology
which is also a separation in
. Equivalently, if
is connected then so is
.