
Re: A toy conjecture which may lead to an other breakthrough conjecture  help request
Posted:
Sep 6, 2013 10:38 PM


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.

