Let $X$ be a separable complete metric space. Let $E$ be a dense subset of $X$ and fix $p\in X$.
I want to 'choose' an element for each $\overline{B(p,1/n)}\cap E$ in ZF. ($n\in \mathbb{Z}^+$)
Is it possible?
As you can see in the link; Constructing a choice function in a complete & separable metric space
It's possible to choose representatives for $\overline{B(p,1/n)}$ for each $n\in \mathbb{Z}^+$.