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Re: A proposition about filters on cartesian product of two sets
Posted:
Nov 1, 2013 2:24 PM


Victor Porton wrote:
> 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.
I've found myself that the statement is false:
http://math.stackexchange.com/questions/547269/apropositionaboutfiltersoncartesianproductoftwosets



