Weak Hausdorff space

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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.

The notion was introduced by M. C. McCord[2] 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.


  1. ^ Hoffmann, Rudolf-E. (1979), "On weak Hausdorff spaces", Archiv der Mathematik 32 (5): 487–504, doi:10.1007/BF01238530, MR 547371 .
  2. ^ McCord, M. C. (1969), "Classifying spaces and infinite symmetric products", Transactions of the American Mathematical Society 146: 273–298, doi:10.2307/1995173, MR 0251719 .