Talk:Quotient Space of Real Line may be Indiscrete

Would it be worth proving that there's an uncountable indiscrete quotient space of the real line? Specifically, if $x \sim y \iff x - y \in \Q$ then since each equivalence class $x + \Q$ is dense in $\R$, the only non-empty open set in $\R/{\sim}$ is the whole space. --Dfeuer (talk) 02:38, 11 March 2013 (UTC)

I don't know, can you find it in any of the books you have been asked to use as source references? --prime mover (talk) 06:12, 11 March 2013 (UTC)