Two new conjectures
Conjecture If $latex a\times^{\mathsf{RLD}} b\subseteq(\mathsf{RLD})_{\mathrm{in}} f$ then $latex a\times^{\mathsf{FCD}} b\subseteq f$ for every funcoid $latex f$ and atomic f.o. $latex a$ and $latex b$ on the source and destination of $latex f$ correspondingly. A stronger conjecture: Conjecture If $latex \mathcal{A}\times^{\mathsf{RLD}} \mathcal{B}\subseteq(\mathsf{RLD})_{\mathrm{in}} f$ then $latex \mathcal{A}\times^{\mathsf{FCD}} \mathcal{B}\subseteq f$ for every funcoid $latex f$ and $latex \mathcal{A}\in\mathfrak{F}(\mathrm{Src}\,f)$, […]
A new conjecture about funcoids and reloids
I’ve forgotten this conjecture when wrote Funcoids and Reloids article: Conjecture $latex (\mathsf{RLD})_{\mathrm{in}} (g\circ f) = (\mathsf{RLD})_{\mathrm{in}} g\circ(\mathsf{RLD})_{\mathrm{in}} f$ for every composable funcoids $latex f$ and $latex g$. Now this important conjecture is in its place in the article. I am going also to spend some time attempting to prove it.
The article “Conjecture: Upgrading a multifuncoid”
I first formulated the conjecture about upgrading a multifuncoid in this blog post. Now I’ve put online an article which is essentially the blog post with added proofs for the cases of n=0,1,2, converted into PDF format. (The conjecture is open for the case n=3 and above.) The terms multifuncoid and upgrading are defined in […]
A new conjecture about funcoids
Conjecture For every composable funcoids $latex f$ and $latex g$ we have $latex g \circ f = \bigcap \{ \uparrow^{\mathsf{FCD} ( \mathrm{Src}\,f ; \mathrm{Dst}\,g) } ( G \circ F ) \hspace{0.5em} | \hspace{0.5em} F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \}$.
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 […]
I submit theory of filters to IJPAM
I previously submitted my article about filters on posets to Armenian Journal of Mathematics. I waited for review of my article about 17 months and they haven’t replied. So I withdraw my submission and now am submitting to an other journal, International Journal of Pure and Applied Mathematics.
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. $latex \mathcal{A}$, […]