 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2014/1/a/i/solution

f : M \to N

is a bijection for which both

f

and

f^{- 1}

f homeomorphism ⟺ f bijective and f, f^{- 1} continuous .

Continuity of a bijection alone is insufficient: continuity of the inverse is a separate requirement.

 New to topics? Read the docs here!