Do we need to provide a composite function when defining a composition of two homeomophisms?
That is,clearly (0,1) is homeormophic to (a,b) and R is homeomorphic to (0,1).In these cases I define a function for each case and show that they are bijective and bi-cts. So what I'm trying to do is defining a composition of these two homeomorphisms,so that R is homeomorphic to (a,b).
So in that case,do I need to provide a function as I do for the above homeomorphisms?