Cone in topological space Homotopy problem

[JoeSabs]

Homework Statement

Let Y be a topological space. Let CY denote the cone on Y.

(a) Show that any 2 continuous functions f, g : X --> CY are homotopic.
(b) Find (pi)1 (CY, p).

Homework Equations

I have no idea. The professor said one problem would be way out in left, to see who could make the connections. I can't. lol

The Attempt at a Solution

See 2.!

I know I haven't made an attempt, so I'm not asking for an answer. Any hints or help is much appreciated.

 

[ystael]

Remember that if two functions f, g are each homotopic to another function k, then you can compose the homotopies to see that f is homotopic to g. Keeping that in mind, can you find a function k: X \to CY which is special somehow, and useful for making homotopies in this way?

Part (b) is an easy corollary of part (a).