On page 58 of Mark Hovey's book *Model Categories*, he states the following definitions:



> 
> "A subset $U$ of a space $X$ is
>  compactly open if for every continuous
>  $f:K\rightarrow X$ where $K$ is
>  compact Hausdorff, $f^{-1}(U)$ is open
>  in $K$... A space $X$ is called a
>  $k$-space, ***or Kelley space***, if every
>  compactly open subset is open."
>  (emphasis mine)
> 
> 
> 


My question is whether $k$-spaces are called $k$-spaces for [John L. Kelley](http://en.wikipedia.org/wiki/John_L._Kelley) or for some other reason. A quick google search shows me that Kelley studied these spaces a lot, and that he [wrote about them](http://tocs.ulb.tu-darmstadt.de/740705.pdf) as $k$-spaces.'' I interpret this as evidence that they are not named for him, since it's fairly uncommon to hear about a (good) mathematician X going around calling things by his own name. Further evidence for this is a statement an older professor made to me that $k$-spaces were studied by Mac Lane before Kelley. 


On the other hand, the word Kelleyfication appears in Mac Lane's *Categories for the Working Mathematician* (on page 182 of the first edition) as a way to change the topology on a Hausdorff space in order to make it a $k$-space. Furthermore, Mac Lane calls compactly generated Hausdorff spaces Kelley spaces.



> 
> 1) Can anyone clear this mystery up for me? Does anyone know the first place these spaces appear in the literature, or the first place the category of $k$-spaces was put forth as the ``right'' category of spaces?
> 
> 
> 2) Is it standard in the literature to assume $k$-spaces are Hausdorff?
> 
> 
> 


Hovey does not, but Mac Lane does. I'm curious about whether there is consensus on this issue.



Are k-spaces named for Kelley?
Engelking cites [this paper](http://www.ams.org/journals/proc/1950-001-03/S0002-9939-1950-0036503-X/home.html) as the place where $k$-spaces were introduced, though the author, David Gale, says the notion was first defined by Hurewicz. The $k$ probably refers to the German `kompakt'.


