Let $X$ be a topological space. Let $Y$ be a subset of $X$. We denote by $X/Y$ the quotient space of $X$ identifying any two elements of $Y$.
Let $A$ and $B$ be two finite subsets of $\mathbb R$. Are $\mathbb R/A$ and $\mathbb R/B$ homeomorphic if and only if $|A| = |B|$?