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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




Re: A toy conjecture which may lead to an other breakthrough conjecture  help request
Posted:
Sep 7, 2013 8:48 AM


William Elliot wrote:
> 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?
I was expiring to prove this conjecture:
http://portonmath.wordpress.com/2013/09/01/funcoidsopenmappings/
I proved this important conjecture yesterday.
This conjecture is an analog for funcoids of the statement that in Top there are direct products. It is a very important statement.
>> 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.
It seems that your grammar notes are true. It is not important anymore anyway after I've proved a more general conjecture.
> 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 the lattice of binary relations it cannot be more than one maximum.
> 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?
10pt.
It is not very hard for me to create a version for you with a different font size. (Which size do you want?) But some formulas may probably overflow outside of the paper.
Acrobat Reader can print a range of pages, but only in PostScript (not PDF) format. My Acrobat Reader 9.5.5 for Linux has create an erroneous PostScript file which cannot be read.
To extract a range of pages from a PDF file to an other PDF file, I use "Print" menu item in Okular (probably not available on Windows). You may also try Evince (maybe available for Windows).
>> 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.



