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 […]
Slides about Algebraic General Topology
I prepared PDF slides for quickly familiarizing a reader with Algebraic General Topology. I hope to give a talk with these slides at a math research conference. The current version of this PDF contains 54 slides.
Oblique products, related theorems and conjectures
I updated Funcoids and Reloids article. Now it contains a section on oblique products. It now contains also the following conjectures: Conjecture $latex \mathcal{A} \times^{\mathsf{RLD}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B}$ for some f.o. $latex \mathcal{A}$, $latex \mathcal{B}$. Conjecture $latex \mathcal{A} \times^{\mathsf{RLD}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} \subset \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}$ for some f.o. $latex \mathcal{A}$, […]
Uniformization of funcoids
I’ve put a sketch draft of future research “Uniformization of funcoids” on my Algebraic General Topology page. “Uniformization” is meant to be a generalization of oblique products of filters. This future research may be published as a part of my Funcoids and Reloids article, or (what is more likely) as a separate article.
Oblique product of filters
Funcoids and reloids are my research in the field of general topology. Let $latex \mathcal{A}$ and $latex \mathcal{B}$ are filters. Earlier I introduced three kinds of products of filters: funcoidal product: $latex \mathcal{A}\times^{\mathsf{FCD}}\mathcal{B}$; reloidal product: $latex \mathcal{A}\times^{\mathsf{RLD}}\mathcal{B}$; second product: $latex \mathcal{A}\times^{\mathsf{RLD}}_F\mathcal{B}$; The last two products are reloids while the first is a funcoid. Funcoidal and […]
“Funcoids and Reloids” preprint is almost ready
Editing of the article Funcoids and Reloids led to almost ready preprint. I can’t publish it just now because it refers to not yet published article Filters on Posets and Generalizations. Note that I moved some theorems from Funcoids and Reloids to Orderings of filters in terms of reloids, because proofs of these theorems rely […]
“Funcoids and Reloids” rewritten
I have checked the new version of the article Funcoids and Reloids for errors. I don’t warrant zero errors, but this version should be neat and readable. Now the new version is considered stable and is the main article referred from Algebraic General Topology homepage. The new version accomplishes this rewriting plan that is instead […]
“Funcoids and Reloids” updated
I updated the development version of my draft article “Funcoids and Reloids” at my Algebraic General Topology page. The new version of the article benefits adding the following notations for a funcoid $latex f$: $latex \langle f \rangle^{\ast}$ $latex [ f ]^{\ast}$ See the article for the meaning of this new notation.