I'm having trouble doing exercise 7.43.6.c of Munkres' Topology. It says:
Show that an open subspace of a topologically complete space is topologically complete.
Now, why isn't the open interval (0,1), considered as a subspace of R, a counterexample to what the question is afirming? (since the sequence 1/n is a Cauchy sequence that converges to 0, a point which isn't in (0,1))