1. The problem statement, all variables and given/known data For any [itex] a \in \left( -1,1 \right) [/itex] construct a homeomorphism [itex] f_a: \left( -1,1 \right) \longrightarrow \left( -1,1 \right) [/itex] such that [itex] f_a\left( a \right) = 0 [/itex]. Deduce that [itex] \left( -1,1 \right) [/itex] is homogeneous. 2. Relevant equations Definition of a homogeneous topological space, ie that the exists a homeomorphism for each pair of points x,y which maps x to y. 3. The attempt at a solution I can't find a set a functions which map an arbitrary point to zero and is surjective. My attemps include f = x - a, f = |x - a|, f = sin (x-a) but these are not homeomorphic for arbitrary a.