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

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William Elliot

Posts: 1,608
Registered: 1/8/12
Re: Please nominate me for Abel Prize
Posted: Jul 17, 2013 11:50 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wed, 17 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.)


What's an improper filter?

(A,B,F) is a reloid when F is a filter for AxB or an improper filter for AxB.

> 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:


Skip the TeX is these ascii only newsgroup; it make reading harder.

Let FF(A) = { F | F filter over A }. Are improper filters included?

> 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).


If S is a set, B subset P(S), then
filter< B > is the filter for S generated by B.

(A,B,f,g) is a funcoid when f:FF(A) -> FF(B), g:FF(B) -> FF(A),
for all X in FF(A), Y in FF(B),
filter< Y \/ f(X) > proper subset P(B)
iff fllter< X \/ g(Y) proper subset P(A)

(A,B,f,g) is a funcoid when f:FF(A) -> FF(B), g:FF(B) -> FF(A),
for all X in FF(A), Y in FF(B),
filter< Y \/ f(X) > = P(B) iff fllter< X \/ g(Y) > = P(A).
Is that correct?

> See http://nlab.mathforge.org/nlab/show/funcoid for a more understandable
> definition of funcoids than one in the paragraph above of this post.


No thanks, I've not the patience to mess with pdf stuff.


Date Subject Author
7/15/13
Read Please nominate me for Abel Prize
Victor Porton
7/16/13
Read Re: Please nominate me for Abel Prize
William Elliot
7/16/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/16/13
Read Balhtam nominates you for the fake Nobel in funconomics
Brian Q. Hutchings
7/16/13
Read Re: Balhtam nominates you for the fake Nobel in funconomics
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
William Elliot
7/17/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
William Elliot
7/18/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/16/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/16/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/16/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/16/13
Read Re: Please nominate me for Abel Prize
William Elliot
7/17/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
grei
7/17/13
Read Re: Please nominate me for Abel Prize
William Elliot
7/17/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/17/13
Read Re: Please nominate me for Abel Prize
Dave L. Renfro
7/17/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/17/13
Read Re: Please nominate me for Abel Prize
Dave L. Renfro
7/17/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/17/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/17/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/17/13
Read please don't nominate me for TetrahedronometrY; thank YoU
Brian Q. Hutchings
7/17/13
Read Re: Please nominate me for Abel Prize
Jens Stuckelberger
7/18/13
Read Re: Please nominate me for Abel Prize
Peter Percival
7/19/13
Read Re: Please nominate me for Abel Prize
FredJeffries@gmail.com
7/19/13
Read Re: Please nominate me for Abel Prize
Victor Porton
7/19/13
Read Re: Please nominate me for Abel Prize
magidin@math.berkeley.edu
7/19/13
Read Re: Please nominate me for Abel Prize
fom
7/19/13
Read Re: Please nominate me for Abel Prize
Victor Porton

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