The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Victor Porton

Posts: 621
Registered: 8/1/05
A proposition about filters on cartesian product of two sets
Posted: Nov 1, 2013 11:29 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

From my question at

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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.