Comments for Victor Porton's Math Blog
https://portonmath.wordpress.com
Math research of Victor PortonTue, 23 May 2017 18:40:43 +0000hourly1http://wordpress.com/Comment on A conjecture about funcoids on real numbers disproved by porton
https://portonmath.wordpress.com/2017/05/22/funcoids-on-real-numbers-solved/#comment-1441
Tue, 23 May 2017 18:40:43 +0000http://portonmath.wordpress.com/?p=2693#comment-1441“The proof isn’t yet thoroughly checked for errors.” Yes, and I found an error in the proof. I am now working on correcting this error.
]]>Comment on Three (seemingly not so difficult) new conjectures by porton
https://portonmath.wordpress.com/2017/05/09/three-new-conjectures-2/#comment-1437
Tue, 09 May 2017 19:47:17 +0000http://portonmath.wordpress.com/?p=2663#comment-1437All three conjectures follow from the fact that is a sublattice of .
]]>Comment on Three (seemingly not so difficult) new conjectures by porton
https://portonmath.wordpress.com/2017/05/09/three-new-conjectures-2/#comment-1436
Tue, 09 May 2017 19:07:25 +0000http://portonmath.wordpress.com/?p=2663#comment-1436I’ve proved the first one. I am going to publish the (easy) proof soon.
]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1428
Tue, 18 Apr 2017 19:50:19 +0000http://portonmath.wordpress.com/?p=2642#comment-1428The proof at https://conference.portonvictor.org/wiki/Funcoid_bases/Disproof was with an error, but the proof idea was right. Now it contains the corrected proof.
]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1427
Tue, 18 Apr 2017 19:29:50 +0000http://portonmath.wordpress.com/?p=2642#comment-1427The conjecture was declined with a counter-example https://conference.portonvictor.org/wiki/Funcoid_bases/Disproof

It yet remains the question whether the condition “1” implies “2”.

]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1425
Tue, 18 Apr 2017 16:25:12 +0000http://portonmath.wordpress.com/?p=2642#comment-1425Can the same counter-example as in https://conference.portonvictor.org/wiki/Funcoid_bases/Failed_condition (the topic of the previous comment) be applied to some implications between conditions 1, 2, 3?
]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1424
Tue, 18 Apr 2017 16:09:05 +0000http://portonmath.wordpress.com/?p=2642#comment-1424The condition “ is a filter on the lattice and is an upper set” is not enough for existence of such that . See https://conference.portonvictor.org/wiki/Funcoid_bases/Failed_condition in the wiki. So the condition “4” is removed from consideration.
]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1422
Sun, 16 Apr 2017 23:10:29 +0000http://portonmath.wordpress.com/?p=2642#comment-1422Should we also add to “4” the requirement for to be filter-closed? (see my book for a definition of being filter-closed).
]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1421
Sun, 16 Apr 2017 21:53:32 +0000http://portonmath.wordpress.com/?p=2642#comment-1421Added condition “4” defined above to the main wiki page. It is quite obvious that and .
]]>Comment on A new research project (a conjecture about funcoids) by porton
https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/#comment-1420
Sat, 15 Apr 2017 21:41:29 +0000http://portonmath.wordpress.com/?p=2642#comment-1420It is easy to show that being a filter is not enough for the (other) conditions of the conjecture to hold (for a counter-example consider and thus ).

Probably the following is equivalent to the conditions of the conjecture: is a filter on and is an upper set.