Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Unsorted
Keywords: filters
Recomm. for undergrads: no
Posted by: porton
on: November 29th, 2009
Solved by: Porton, Victor
Conjecture   Let $ a $ and $ b $ are filters on a set $ U $ and $ a\cap b = \{U\} $. Then $$\exists A\in a,B\in b: (\forall X\in a: A\subseteq X \wedge \forall Y\in b: B\subseteq Y \wedge A \cup B = U).$$

See here for some equivalent reformulations of this problem.

This problem (in fact, a little more general version of a problem equivalent to this problem) was solved by the problem author. See here for the solution.

Maybe this problem should be moved to "second-tier" because its solution is simple.

* indicates original appearance(s) of problem.


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