Understanding Serge Lang's Definition of Homotopy I have been following Serge Lang's Complex Analysis text book and today I came across a chapter on homotopy. I have trouble visualising and honestly, understanding the definition that he has given in his book. Here is the definition from his book 
Could somebody explain to me how I can visually interpret this? I would also be really grateful if someone had a graphic or visual that would illustrate what is meant in this definition. Any help will be appreciated.

You can see each $f_x(t)=\psi(t,x)$ as a continuous family of paths, indexed by the points in the interval $[c,d]$.  The conditions mean that the initial path $f_c(t)$ is precisely $\gamma(t)$ and the final path is $\eta(t)$.
