Solution
= Solution
Any two nonempty <open> sets of $Y$ are cofinite by part (iii). Their complements have <finite union>, so the two sets must intersect because $Y$ is infinite. Thus $Y$ is a <hyperconnected space>.
A <Hausdorff space> with at least two points has disjoint nonempty <open> neighbourhoods of two distinct points. This is impossible here. Therefore \b[$Y$ is not <Hausdorff>].