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A proposition about filters on cartesian product of two sets
Posted:
Nov 1, 2013 11:29 AM


From my question at math.stackexchange.com: http://math.stackexchange.com/questions/547269/apropositionaboutfiltersoncartesianproductoftwosets
I call reloid a filter on a cartesian product of two sets.
I define product AxB of two filters A and B as the reloid generated by the filter base {XxY  X in A, Y in B}.
Please help to prove:
/\{AxB  B in T}=A x /\T for every filter A and set T of filters.
(/\ is set intersection.)
I need this to finish the proof that product of filters (with left argument being a fixed filter) is an (antitone) lattice homomorphism. I further need this to prove that certain categories are cartesian closed. Well, this is an other story.
The question is important for proving some categories are cartesian closed. So sorry for crossposting.



