:::::::Oh, this is probably an old argument about whether compact means Hausdorff and quasi-compact or not.  Kelley and Willard seem to like non-Hausdorff compact spaces, so with some small mention of the other convention, I think it'd be fine to expand the coverage.  Did my recent edit address this?  I think it is good to mention the "downside" to the A.e. but the old lead seemed to contradict the compactification article's (and getspaper's) reasonable definition.