Consider the category of (proximally) continuous maps (entirely defined monovalued functions) between endo-funcoids. Remind from my book that morphisms $latex f: A\rightarrow B$ of this category are defined by the formula $latex f\circ A\sqsubseteq B\circ f$ (here and below by abuse of…

read moreI am (re)reading Bourbaki “General Topology” (in Russian language). Despite I am a general topologist, I have never had a systematic general topology study. I think now I should fill this hole. Maybe after reading Bourbaki I will return to Johnstone “Stone…

read moreI’ve put online my rough partial draft of the theory of bijective correspondence between frames/locales and certain pointfree funcoids. Pointfree funcoids are a massive generalization of locales and frames: They not only don’t require the lattice of filters to be boolean but…

read moreI have read The point of pointless topology today and am going to study the book Johnstone “Stone Spaces” which I purchased maybe a year or two ago. The purpose of this study is to integrate others’ pointless topology with my theory…

read moreI addition to this conjecture I formulate one more similar conjecture: Conjecture $latex a\setminus^{\ast} b = a\#b$ for arbitrary filters $latex a$ and $latex b$ on a powerset cannot be proved in ZF (without axiom of choice). Notation (where $latex \mathfrak{F}$ is…

read moreConjecture Distributivity of the lattice $latex \mathsf{FCD}(A;B)$ of funcoids (for arbitrary sets $latex A$ and $latex B$) is not provable in ZF (without axiom of choice). It is a remarkable conjecture, because it establishes connection between logic and a purely algebraic equation….

read moreIn this blog post I announced that I am going to change the definition of order of pointfree funcoids in my book. Now in the last preprint the changes are done.

read moreIn my preprint I defined pre-order of pointfree funcoids by the formula $latex f\sqsubseteq g \Leftrightarrow [f]\subseteq[g]$. Sadly this does not define a poset, but only a pre-order. Recently I’ve found an other (non-equivalent) definition of an order on pointfree funcoids, this…

read moreI have shown in my research monograph that topological (even pre-topological) spaces are essentially (via an isomorphism) a special case of endo-funcoids. It was natural to suppose that locales or frames induce pointfree funcoids, in a similar way. But I just spent…

read moreI remind that I am not a professional mathematician. Nevertheless I have written research monograph “Algebraic General Topology. Volume 1”. Yesterday I have asked on MathOverflow how to characterize a poset of all filters on a set. From the answer: the posets…

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