Let $X$ be a topological space and $Y $ be the upper open hemisphere. Prove that any two maps $f, g:X \to Y$ are homotopic.
I have just started to learn algebraic topology and just learn the definition and few example of homotopy.
Here I need to find a function $F:X \times I \to Y$ such that $F(x,0)=f(x)$ and $F(x,1)=g(x)$
But I could not find such a function. Can somebody help me please.
Are there any general way to find a homotopic function?
Thanks for your time