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Topic: Please nominate me for Abel Prize
Replies: 33   Last Post: Jul 19, 2013 10:22 PM

 Messages: [ Previous | Next ]
 Victor Porton Posts: 621 Registered: 8/1/05
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