# Weak Hausdorff space

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.[1] In particular, every Hausdorff space is weak Hausdorff. As a separation property, it is stronger than T_{1} (which says that points are closed): every weak Hausdorff space is a T_{1} space.[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.

## References

- Hoffmann, Rudolf-E. (1979), "On weak Hausdorff spaces",
*Archiv der Mathematik*,**32**(5): 487–504, doi:10.1007/BF01238530, MR 0547371. - J.P. May,
*A Concise Course in Algebraic Topology*. (1999) University of Chicago Press ISBN 0-226-51183-9*(See chapter 5)* - Strickland, Neil P. (2009). "The category of CGWH spaces" (PDF).
- McCord, M. C. (1969), "Classifying spaces and infinite symmetric products",
*Transactions of the American Mathematical Society*,**146**: 273–298, doi:10.2307/1995173, JSTOR 1995173, MR 0251719.

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