> 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.
(F,X,Y)^-1 is useful when we assign f=(F,X,Y). This way we have a definition for the morphism f^-1.
> 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.
Well, if you do NOT use reverse order which I recommend.
> 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)?
It becomes a trivial set-theoretic equation if we replace /\ -> \/
(\/_j Fj) xx G = \/_j (Fj xx G)?
It seems for me that you have confused a poset with the dual poset. However I am not sure what you do mean.
> 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.