Main Question or Discussion Point
I have a question about the definition of null homotopic. My textbook (Functions of one Complex Variable I by John B. Conway) defines it as follows: If [tex]\gamma[/tex] is a closed rectifiable curve in a region G, then [tex]\gamma[/tex] is homotopic to zero if [tex]\gamma[/tex] is homotopic to a constant curve. My question is, if G is simply connected, then is [tex]\gamma[/tex] homotopic to ANY constant curve in G? This seems obvious to me, but I'm not sure if I should prove it or just state it.