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.

By definition, $\psi(t,c)=\gamma(t)$. Since $\psi$ is continuous, if $c_1$ is slightly bigger than $c$, then $t\mapsto\psi(t,c_1)$ is a path which is close to $\gamma$. And if $c_2$ is slightly bigger than $c_1$, then $t\mapsto\psi(t,c_2)$ is a path which is close to the previous one. And so on, until you reach $d$. So, $\psi$ deforms $\gamma$ into $\eta$.
