Are there any general properties or rules for a product of a topological space and compact space to admit a compactification?
I am usually assuming Hausdorff compactifications, so the original space must by Tychonoff to admit a compactification. But this is just a matter of convention I guess. So in my question, I am asking for other requirements.
Also, generally, what properties of a general topological space can imply it will have compactifications? I am aware that any topological space can have Stone-Čech and that locally compact space can have Alexandroff one-point compactification, but what about other types of compactifications?
Thank you.