Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Which term to choose?
Replies: 41   Last Post: Nov 9, 2013 5:20 AM

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
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/algebraic-general-topology.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.
>

Date Subject Author
10/25/13 Victor Porton
10/25/13 Peter Percival
10/25/13 fom
10/25/13 William Elliot
10/26/13 William Elliot
10/26/13 Victor Porton
10/26/13 William Elliot
10/27/13 Victor Porton
10/27/13 William Elliot
10/28/13 Victor Porton
10/29/13 William Elliot
10/29/13 Victor Porton
10/30/13 William Elliot
10/30/13 Victor Porton
10/30/13 William Elliot
10/31/13 Victor Porton
11/1/13 William Elliot
11/1/13 Victor Porton
11/1/13 William Elliot
11/2/13 Victor Porton
11/2/13 William Elliot
11/3/13 Victor Porton
11/3/13 Victor Porton
11/3/13 William Elliot
11/4/13 William Elliot
11/4/13 Victor Porton
11/5/13 William Elliot
11/5/13 Victor Porton
11/6/13 William Elliot
11/6/13 Victor Porton
11/6/13 William Elliot
11/7/13 Victor Porton
11/7/13 William Elliot
11/8/13 William Elliot
11/8/13 Victor Porton
11/8/13 William Elliot
11/9/13 Victor Porton
11/9/13 William Elliot
11/9/13 William Elliot
11/9/13 Victor Porton
10/26/13 Victor Porton