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Topic: A proposition about filters on cartesian product of two sets
Replies: 1   Last Post: Nov 1, 2013 2:24 PM

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Victor Porton

Posts: 520
Registered: 8/1/05
Re: A proposition about filters on cartesian product of two sets
Posted: Nov 1, 2013 2:24 PM
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Victor Porton wrote:

> From my question at math.stackexchange.com:
> http://math.stackexchange.com/questions/547269/a-proposition-about-filters-on-cartesian-product-of-two-sets
>
> 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 cross-posting.


I've found myself that the statement is false:

http://math.stackexchange.com/questions/547269/a-proposition-about-filters-on-cartesian-product-of-two-sets



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