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




Re: Order, Filters and Reloids
Posted:
Aug 26, 2013 10:11 PM


> > 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/algebraicgeneraltopology.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.



