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Topic: Order, Filters and Reloids
Replies: 11   Last Post: Sep 1, 2013 10:54 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Order, Filters and Reloids
Posted: Aug 26, 2013 10:11 PM
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> > In what follows, "filter" will mean a filter in the usual sense
> > or the improper maximum filter P(S).


> > The product of filters is associative.
>
> No, it is associative up to an isomorphism.
> I have no formal proof for this, yet.


I've a proof for that using
Ax(BxC) = AxBxC = (AxB)xC
or simply
A x BxC = AxBxC = AxB x C.

> > The composition of reloids is associative.
>
> Correct. Theorem 7.13 in my book:
> http://www.mathematics21.org/algebraic-general-topology.html


How many thorems of chapter 7 are about reloids only?
Other than what is mentioned here, what are some of them?

> > If A is a set of filters for X, B a set of filters for Y, then
> > /\{ FxxG | F in A, G in B } = /\A xx /\B.

>
> Yes, theorem 7.22 in my book.
>

> > The composition of two complete reloids is complete.
>
> It is a conjecture.





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