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,

, if every compactly open subset is open." (emphasis mine)or Kelley space

My question is whether $k$-spaces are called $k$-spaces for 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 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.