, a weak Hausdorff space
is a topological space
where the image of every continuous map from a compact Hausdorff space
into the space is closed. In particular, every Hausdorff space is weak Hausdorff.
The notion was introduced by M. C. McCord to remedy an inconvenience of working with the category of Hausdorff spaces. It is often used in tandem with compactly generated spaces in algebraic topology.