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In Rezk - Compactly generated spaces a k-Hausdorff property is defined, between weakly Hausdorff and unique sequential limits.

On the other hand, a stronger notion of k-Hausdorff between $T_2$ and compacts are closed was already in use in the literature, e.g. Lawson and Madison - Quotients of k-semigroups.

Has the weaker k-Hausdorff property appeared in the literature beyond Rezk's nlab note? The preamble seemed to indicate it was novel. See also some discussion at Math.SE.

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  • $\begingroup$ Your references seem to use a non-math-mode k, so I edited accordingly. I hope that was correct. $\endgroup$
    – LSpice
    Commented Sep 2, 2023 at 2:13
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    $\begingroup$ Just to make things clear, the weaker version of k-Hausdorff is the one from Rezk. $\endgroup$
    – PatrickR
    Commented Sep 2, 2023 at 2:58
  • $\begingroup$ It was used and studied in several papers around the early 70s. One such is B. Day's paper Limit spaces and closed span categories published 1974. Another is the paper Comparisons of notions of weak Hausdorffness by Lawson and Madison, which is found in conference proceedings from 1975 and seems to be difficult to get hold of. I'd suggest that the definition is probably folklore that emerged from the late 60s. $\endgroup$
    – Tyrone
    Commented Sep 2, 2023 at 5:46
  • $\begingroup$ Thanks Tyrone. I found this review for the proceedings reference, clearly referencing the property: zbmath.org/0345.54025 $\endgroup$
    – Steven Clontz
    Commented Sep 2, 2023 at 14:17

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To not leave my question unanswered, I'll note that @Tryone suggested a couple of references in comments to the question.

In particular, while I do not have a copy of the paper itself, this zbMath review seems to clearly suggest the authors investigated both notions of k-Hausdorff.

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