Hi!

I have problems to proof this one:

Let Y be a closed subset of a manifold Q, $\displaystyle p: E \rightarrow B$ a vector bundle and E* the one-point compactification of E. Then $\displaystyle f,g: Q \rightarrow E^{*}-B$ which agree on Y are homotopic relative Y.

It is clear that E*-B is contractible. From the homotopy extension theorem we can extend the homotopy (f=g on Y) to all of Q, but why can we choose it in a way that it starts at f and ends at g?

best greetings