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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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Victor Porton

Posts: 529
Registered: 8/1/05
Re: Please nominate me for Abel Prize
Posted: Jul 18, 2013 7:56 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

William Elliot wrote:

> 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?


Improper filter on a set A is the set A itself.

> (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?


Yes, in all my works improper filter is included.

By the way, it was somebody's stupid idea to exclude improper filter from
the set of filters.

>> 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)


Yes.

> (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?


Yes.

Two definitions which you presented are equivalent to each other.

>> 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.


The above link is HTML with MathML, not PDF.

--
Victor Porton - http://portonvictor.org


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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