This is a follow-up to Dan Ramras' answer of [this question](https://mathoverflow.net/questions/47702/why-the-w-in-cgwh-compactly-generated-weakly-hausdorff-spaces).


The following correction can be found in the errata to [The Geometry of Iterated Loop space](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.170.2840&rep=rep1&type=pdf) (Page 484 [here](http://www.math.uchicago.edu/~may/BOOKS/homo_iter.pdf)).



> 
> The weak Hausdorff rather than the Hausdorff property should be required of spaces [...] in order to validate some of the limit arguments used [...].
> 
> 
> 


I was not able to figure out which type of "limit arguments" really would have needed the weak Hausdorff condition instead of the regular one used in the original paper and would be happy to understand the necessity of the correction, ideally by means of an explicit example in the paper.



Why should have Peter May worked with CGWH instead of CGH in "The Geometry of Iterated Loop Space"?
I'm not quite certain what Peter May had in mind 40 years ago,
but probably he had in mind the fact that pushouts are a lot better
behaved in CGWH than in CGH. Specifically, CGWH is closed
under pushouts, one leg of which is the inclusion of a closed
subspace. CGH does not have such nice behavior, and pushouts
like that are used all over The Geometry of Iterated Loop Spaces,
specifically in the construction of a monad from an operad and
in the use of geometric realizations of simplicial spaces.


