Conjecture: Upgrading a multifuncoid
This short article is the first my public writing where I introduce the concept of multidimensional funcoid which I am investigating now. But the main purpose of this article is to formulate a conjecture (see below). This is the shortest possible writing enough to explain my conjecture to every mathematician. Refer to this Web site […]
My research is stalled
My research of n-ary funcoids is stalled now, as I am (yet) unable to solve certain problem. I posted a special version of this problem to MathOverflow. Please help me to solve this open problem. It is a very important problem.
Preliminary announce: n-ary funcoids
I am now developing a theory of generalization of funcoids, n-ary (multi)funcoids (where n is a set). Previously I was going to make first theory of finitary multifuncoids that is the case when n is finite, because there were some complexities with proving some important theorems about infinitary funcoids. Today I managed to prove it […]
“Pointfree Funcoids” is now a good draft
I updated online article “Pointfree Funcoids” from “preliminary draft” to just “draft”. This means that it was somehow checked for errors and ready for you to read. (No 100% warranty against errors however.) Having finished with that draft the way is now free for my further Algebraic General Topology research, such as n-ary (multidimensional) funcoids, […]
Draft: Pointfree funcoids
My draft article Pointfree Funcoids was not yet thoroughly checked for errors. However at this stage of the draft I expect that there are no big errors there only possible little errors. Familiarize yourself with Algebraic General Topology.
Pointfree funcoids – a category
I updated the draft of my article “Pointfree Funcoids” at my Algebraic General Topology site. The new version of the article defines pointfree funcoids differently than before: Now a pointfree funcoid may have different posets as its source and destination. So pointfree funcoids now form a category whose objects are posets with least element and […]
Pointfree funcoids
I put on the Web the first preliminary draft of my article “Pointfree Funcoids”. It seems that pointfree funcoids is a useful tool to research n-ary (multidimensional as opposed to binary) funcoids which in turn is a useful tool to research operations on values of generalized limits of n-ary functions. See Algebraic General Topology for […]
My research plans shifted
Yesterday I wrote that I next thing which I will research are n-ary funcoids and n-ary reloids. It seems that (n+m)-ary funcoid can be split into a funcoid acting from n-ary funcoids to m-ary funcoids (similarly to (n+m)-ary relation can be split into a binary relation between n-ary tuples and m-ary tuples). But this funcoid […]