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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 28, 2013 11:26 PM
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On Tue, 27 Aug 2013, Victor Porton wrote:
> William Elliot wrote:
>

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

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

>
> Have you noticed that chapter 7 is titled "Reloids"? All theorems in this
> chapter are about reloids.


I'm sill hassling with the weirdly written section "Funcoids and Reloids". PDF
files are a pain in the butt, hard to work with. I've yet to get anything out
of it except noticing weird unneeded notations and definitions that make it
all the more complicated.

For example, what's (F,X,Y)^-1? Wouldn't it simply be (F^-1,Y,X)?
Your definition of (F,X,Y)^-1 was unduly confusing and muddled.

In addition, there's no efficient way to write and
comment about interesting parts.

If F,G in Ft(X), H in Ft(Y), it's straight forward to prove
F/\G xx H = FxxH /\ GxxH.

Without referring to your pdf file, how do you prove:
if, for all j, Fj in Ft(X), G in Ft(y), then
(/\_j Fj) xx G = /\_j (Fj xx G)?

The same method used for the finite case, can't be reworked for the infinite
case. BTW, the proposition is false if the index set for j is empty.






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