A mapf:MNisopenif for each open setUM, the image setf(U) is open inN. (c)Iffis an open, continuous bijection, is it a homeomorphism? (d)Iff:RRis a
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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?

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