Due my research about singularities the problem formulated in this blog post was solved negatively with help of Alex Ravsky who has found a counter-example. The conjecture was: $latex \mathrm{GR}(\Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections. The counter-example follows: $latex f=\{(x,y)\in\mathbb…
read moreI’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…
read moreI 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…
read moreI 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.
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Algebraic general topology Category theory Filters General Topology Open problems Pointfree topology
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….
read moreOn 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]]
read moreI feel that there are certain similarities between God and time machine. Please read and discuss at this tiddler.
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Algebraic general topology General Topology Math on the Web Nonsmooth analysis Open problems Pointfree topology
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…
read moreToday 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.
read moreI’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 $latex A_0$, $latex B_0$, $latex A_1$,…
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