I am reading through a book on topology and came across the following phrase: for each element $x\in X$ we can uniquely define a function $f_x: A\rightarrow B$ such that $f_x$ satisfies some topological property $P$.
What exactly does this mean? Does this mean that for each $x\in X$ there is only one $f_x$ satisfying the property $P$? Or does it mean that if you have different elements $x\neq y$ in $X$ then $f_x\neq f_y$?
The terminology is a bit confusing to me.