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…

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.

read moreThere 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.

read moreI 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 $latex A_0$, $latex B_0$, $latex A_1$,…

read moreI’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…

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