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.