
Principal Reliods
Posted:
Oct 30, 2013 4:48 AM


On Tue, 29 Oct 2013, Victor Porton wrote: > William Elliot wrote: > > 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.
Is this corect? F is ia principal reloid for XxY when F is the principal filter of AxB for some A subset X, B subset Y.
Though all principal reloids are principal filters, there are some principal filters that aren't principal reloids. Have you a example?
> This correspondence also maps composition of binary relations to composition > of reloids (easy to show).
There's also a bijection between principle filters for a product and binary relations of the product. Is this also isomorphic like?
> So we have kinda isomorphism between binary relations and principal reloids.
For composition and finite intersections but not infinite intersections.
Are there any theorems true for principal reloid for a product that fail for pricnipal filters for the product?
> > It seems there's enough material about reloids for a short paper. > > Seriously, why to write such a paper when there is already a whole book? The book is too long and complex to get the attention of many people. It also needs to be recased into existing notation and terminalogy.
> Moreover reloids are closely related with funcoids, and to consider reloids > without funcoids would be wrong.
Isn't there some use of reloids per se?
> 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) Is this just the chapters on funcoids and reloids of your book or is it much different?
> > 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. >

