# Definition of an ultra pre-filter

I have come across the term "ultra prefilter" which has two possible definitions (that I can think of). I tried googling this first I swear! (but google thinks I'm looking for filtered water or a water purifier)

The two most obvious meanings to assign to an ultra prefilter $F$ on a space $X$

• $F$ is a prefilter on $X$ which is not properly contained in any other prefilter on $X$

• $F$ is a prefilter on $X$ which is equivalent to any of its refinements

The first one is simply the definition of an ultra filter applied to a prefilter instead. However the second one seems more appropriate, but I wanted to confirm it before I trust it too deeply.

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