Indiscrete topology
= Indiscrete topology
{title2=$\{\varnothing,X\}$}
The indiscrete topology on a set $X$ has only the empty set and the whole set as <open sets>. When $X$ has more than one point it is not a <Hausdorff space>. For example the <quotient topology> on $\mathbb R/\mathbb Q$ is indiscrete: a nonempty open saturated subset contains an interval and all its rational translates, which cover $\mathbb R$.