
Re: Please nominate me for Abel Prize
Posted:
Jul 17, 2013 9:24 AM


William Elliot wrote:
> On Tue, 16 Jul 2013, Victor Porton wrote: >> William Elliot wrote: > >> Reloid is basically just a filter on a Cartesian product of two sets.
The exact definition:
A reloid is a triple (A;B;F) where A and B are sets and F is a filter on their product AxB.
(Note that I allow a filter to be improper.)
> Definition. > A reloid is a filter for a product of two sets. > > Is that correct and accurate? > > What basically is a funcoid? Or even better, > what, in a line or two, IS a funcoid?
A funcoid is a quadruple $(A;B;a;b)$ where $A$ and $B$ are sets, $a$ is a function from the set of filters on $A$ to the set of filters on $B$, $b$ is a function from the set of filters on $B$ to the set of filters on $A$, subject to the following condition:
For every filter X on A and every filter Y on B, the filter (on B) generated by the union of Y and a(X) is not the entire power set P(B) iff the filter (on A) generated by the union of X and b(Y) is not the entire power set P(A).
See http://nlab.mathforge.org/nlab/show/funcoid for a more understandable definition of funcoids than one in the paragraph above of this post.
 Victor Porton  http://portonvictor.org

