In his 1967 paper *A convenient category of topological spaces*,
Norman Steenrod introduced the category *CGH* of **compactly generated Hausdorff spaces**
as a good replacement of the category *Top* topological spaces, in order to do homotopy theory.

The most important difference between *CGH* and *Top* is that in *CGH* there is a functorial homeomorphism $$\mathrm{map}(X,\mathrm{map}(Y,Z))\cong \mathrm{map}(X\times Y,Z),$$
a fact that is only true in *Top* under the extra assumption that $Y$ is locally compact.

But in more recent papers, I see that people use *CG WH* spaces instead of

*CGH*spaces... Why?

Could someone explain to me what goes wrong in *CGH* spaces
(please illustrate with an example),

and explain how the *"w"* fixes everything?

Also (following Jeff's comment), to whom should the *"w"* be attributed?

One more wish: can someone give me an example of a *CGWH* space that isn't *CGH*?