My proposal for Open Problem Garden
I’ve sent to personnel of Open Problem Garden the following proposal email: Please add in each problem page a PayPal donation button. The money collected for a problem should be directed to the person which first solves the problem. One additional advantage is that this would provide a way to sort problems by importance: most […]
Wiki to prove that certain categories are cartesian closed
I have announced that I have proved that Category of continuous maps between endofuncoids is cartesian closed. This was a fake alarm, my proof was with a crucial error. Now I have put the problem and some ideas how to prove it in a wiki. So I announce a new project akin to Polymath Project. […]
Category of continuous maps between endofuncoids is cartesian closed
I rough draft article I prove that the category of continuous maps between endofuncoids is cartesian closed. Whether the category of continuous maps between endoreloids is cartesian closed, is yet an open problem.
Changes to my article about products in certain categories
There are two changes in Products in dagger categories with complete ordered Mor-sets draft article: 1. I’ve removed the section on relation of subatomic product with categorical product saying that for funcoids they are the same. No, they are not the same. My claim that they are the same was false. 2. Added section “Special […]
A suggested way to solve an open problem
On the task formulated in this blog post: An attempt to prove that $latex \mathrm{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections (see http://portonmath.tiddlyspace.com/#[[Singularities%20funcoids%3A%20some%20special%20cases]]) http://portonmath.tiddlyspace.com/#[[Singularities%20funcoids%3A%20special%20cases%20proof%20attempts]]
Philosophy: God and time machine
I feel that there are certain similarities between God and time machine. Please read and discuss at this tiddler.
A wiki about applying generalized limit to singularities theory
I have created a wiki about development of theory of singularities using generalized limits. Please read my book (where among other I define generalized limits) and then participate in this research wiki. Study singularities in this novel approach and share Nobel Prize with me!
My article has been accepted for publication
Today I’ve received email saying that my article “Funcoids and Reloids: a Generalization of Proximities and Uniformities” has been accepted for publication in European Journal of Pure and Applied Mathematics. See also the preprint of this article.
A new proposition about infimum product
I’ve proved a new simple proposition about infimum product: Theorem Let $latex \pi^X_i$ be metamonovalued morphisms. If $latex S \in \mathscr{P} ( \mathsf{FCD} ( A_0 ; B_0) \times \mathsf{FCD} ( A_1 ; B_1))$ for some sets $latex A_0$, $latex B_0$, $latex A_1$, $latex B_1$ then $latex \bigsqcap \left\{ a \times b \,|\, ( a ; […]
Some new minor results
I’ve proved: $latex \bigsqcap \langle \mathcal{A} \times^{\mathsf{RLD}} \rangle T = \mathcal{A} \times^{\mathsf{RLD}} \bigsqcap T$ if $latex \mathcal{A}$ is a filter and $latex T$ is a set of filters with common base. $latex \bigsqcup \left\{ \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B} \hspace{1em} | \hspace{1em} \mathcal{B} \in T \right\} \neq \mathcal{A} \times^{\mathsf{RLD}} \bigsqcup T$ for some filter $latex T$ and […]