In mathematics, a weak Hausdorff space or weakly Hausdorff space is a topological space where the image of every continuous map from a compact Hausdorff space into the space is closed.
As a separation property, it is stronger than T1, which is equivalent to the statement that points are closed.
[2][3] The notion was introduced by M. C. McCord[4] 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.
For that, see the category of compactly generated weak Hausdorff spaces.
A k-Hausdorff space[5] is a topological space which satisfies any of the following equivalent conditions: A Δ-Hausdorff space is a topological space where the image of every path is closed; that is, if whenever
Every weak Hausdorff space is
This topology-related article is a stub.