1. The problem statement, all variables and given/known data If H:I[tex]\rightarrow[/tex]I is a monotone and continuous function, prove that H is a homeomorphism if either a) H(0) = 0 and H(1) = 1 or b) H(0) = 1 and H(1) = 0. 2. Relevant equations 3. The attempt at a solution So if I can prove H is a homeomorphism for a), b) follows from the fact that the map defined by t[tex]\rightarrow[/tex]H(1-t) is also a homeomorphism because it is the composite of two homeomorphisms. H is obviously one-to-one, but I don't know how to "show" this. At first I figured that I should assume |H(t1)-H(t2)| < [tex]\delta[/tex] for some [tex]\delta[/tex] > 0 and try to show that there exists a [tex]\epsilon[/tex] > 0 such that |t1 - t2| < [tex]\epsilon[/tex]. I didn't know where to go after this, so I tried the sequence definition for continuity and I got nowhere. Any suggestions?