A map f : M → N is open if for each open set U ⊂ M, the image set f(U) is open in N.
(c) If f is an open, continuous bijection, is it a homeomorphism?
(d) If f : R → R is a continuous surjection, must it be open?
(e) If f : R → R is a continuous, open surjection, must it be a homeomorphism?
(f) What happens in (e) if R is replaced by the unit circle S1?