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Two continuous maps $f_0,f_1$ are homotopic if there is a continuous map $F:X\times I\rightarrow Y$ such that $F(x,0)=f_0(x)$ and $F(x,1)=f_1(x)$

So I understand that intuitively two continuous maps $f_0,f_1:X\rightarrow Y$ are homotopic if there is a "continuous translation of one to the other".

However I am bit confused as to how to think of "homotopic relative to a set $A$". To be precise that is:

If there is a homotopy $F:X\times I\rightarrow Y$ between $f_0$ and $f_1$ such that $F(a,t)=f_0(a)$ for all $a\in A$ and all $t\in I$

I'm not really understanding what this definition is telling me?

Thanks for any help