I have solved the first two of these three open problems I proposed, but have no clue how to solve the third. (Actually, I’ve solved only a special case of the second problem, but that’s OK, this special case is enough for…
read moreSee here (especially this draft article) for definition of cross-composition product and quasi-cartesian functions. Conjecture 1 Cross-composition product (for small indexed families of relations) is a quasi-cartesian function (with injective aggregation) from the quasi-cartesian situation $latex {\mathfrak{S}_0}&fg=000000$ of binary relations to the…
read moreIn this blog post I introduced the notion of category with star-morphisms, a generalization of categories which have aroused in my research. Each star category gives rise to a category (abrupt category, see a remark below why I call it “abrupt”), as…
read moreIn my research aroused a new kind of structures which I call categories with star-morphisms. In this blog post I define categories with star-morphisms. For sample usages of star categories see this draft article. Definition 1 A pre-category with star-morphisms consists of…
read moreThe status of the article “Multidimensional Funcoids” is raised from “very rough partial draft” to “rough partial draft”. It means that now you probably can understand this my writing. See my research in general topology.
read moreThe following conjecture seems trivial but I have a hard hour trying to prove it. I suspect I have a big difficulty on the course of my research. Conjecture $latex \prod^{\mathsf{FCD}} a \not\asymp\prod^{\mathsf{FCD}} b \Leftrightarrow \forall i\in n : a_i \not\asymp b_i$…
read moreFirst, we can define product of reloids as a trivial generalization of the alternative definition of product of uniform spaces. There are no trivial simplification of this relatively inelegant definition, it is not algebraic as I would want. I (without any evidence…
read moreIt was my long time dream since the first course of the university to do math analysis in algebraic fashion instead of the notorious epsilon-delta notation overloaded with quantifiers. This dream has been accomplished. I discovered a new math theory in which…
read moreI have proved the conjecture “Upgrading a multifuncoid is multifuncoid”. The proof is currently presented in this online draft article.
read moreI’ve sent this article to an open access peer reviewed journal: A New Kind of Product of Ordinal Number of Relations having Ordinal Numbers of Arguments (the article is available online).
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