Hyperconnected space
= Hyperconnected space
A <topological space> is hyperconnected if any two nonempty <open sets> intersect. Every <continuous map> from a nonempty hyperconnected space to a <Hausdorff space> is constant: two distinct image points would have disjoint open neighbourhoods whose nonempty inverse images contradict hyperconnectedness. Every infinite set with the <cofinite topology> is hyperconnected.