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Topic: A toy conjecture which may lead to an other breakthrough conjecture - help request
Replies: 9   Last Post: Sep 8, 2013 4:10 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: A toy conjecture which may lead to an other breakthrough conjecture
- help request

Posted: Sep 6, 2013 10:38 PM
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On Fri, 6 Sep 2013, Victor Porton wrote:

> Please help with a solution. This is VERY important for development of
> general topology.

Why is it important for topology?

> Let A be a set.
> Let pi_0, pi_1 be projections from AxA.
> Let F_0, F_1, G_0, G_1 be binary relations on A.

> Let phi_A be the maximal binary relation in (AxA) x (AxA) such that
> pi_0 o phi_A subset F_0 o pi_0 and pi_1 o phi_A subset F_1 o pi_1.

Consistent with F_0 being a binary relation on AxA don't you mean
"on"? Indeed, a binary relation on A is not "in" AxA but a subset
of AxA.

Is phi_A the unique maximal relation as implied by the use of
"the" (making phi_A a maximum) or to you mean "_a_ maximal".

In what font size is your pdf book? Can you change it?
What fort sizes can you use? Can Acrobat reader print
a range pages without printing the whole file?

> Prove (or disprove) that Sigma = phi_B o phi_A is the maximal
> binary relation on A such that pi_0 o Sigma subset G_0 o
> F_0 o pi_0 and pi_1 o Sigma subset G_1 o F_1 o pi_1.

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