
Re: Which term to choose?
Posted:
Oct 29, 2013 1:08 PM


William Elliot wrote:
>> >> I wrote a chapter with the proof that for every principal reloid F >> >> F o /\_j Gj = /\{ F o Gj  j in J }. > > What else is in that chapter? More about reloids? > >> > Why a whole chapter? The proof is so short and the topic so basic >> > that it should be included in the basic chapter on reloids. >> > >> > Anyway, that shows that principal reloids with composition >> > are order dual to quantales. >> >> This result is not interesting, because principal reloids are essentially >> the same as binary relations. >> > How so?
It is by definition of principal reloids. A principal reloids is by definition a reloid corresponding to a binary relation. Trivially this correspondence is bijective.
This correspondence also maps composition of binary relations to composition of reloids (easy to show).
So we have kinda isomorphism between binary relations and principal reloids.
>> That binary relations with composition are order dual to quantales, isn't >> a new result. > > It seems there's enough material about reloids for a short paper.
What?! Do you want to plagiarize my work? (kidding)
Seriously, why to write such a paper when there is already a whole book?
Moreover reloids are closely related with funcoids, and to consider reloids without funcoids would be wrong.
In fact such a paper already exists (and it is in peer review now): http://www.mathematics21.org/algebraicgeneraltopology.html "Funcoids and Reloids" (PDF, preprint)
> What intuitive significance would you give reloids?
1. Reloids are a generalization of uniform spaces.
2. Reloids are a generalization of binary relations.
3. Reloids are closely related with funcoids.

