Let X,Y be topological spaces. Consider Z = X x Y and the product topology
genearted by the projections p_x, p_y. Let A be a subset of Z.
Suppose that X,Y are locally path connected. Show that A is connected if
and only if A is path connected.
I just don't know how to prove the below part.
show that if a connected space is also locally path connected, then it is
path connected.
