I’ve put a sketch draft of future research “Uniformization of funcoids” on my Algebraic General Topology page. “Uniformization” is meant to be a generalization of oblique products of filters. This future research may be published as a part of my Funcoids and…
read moreFuncoids and reloids are my research in the field of general topology. Let $latex \mathcal{A}$ and $latex \mathcal{B}$ are filters. Earlier I introduced three kinds of products of filters: funcoidal product: $latex \mathcal{A}\times^{\mathsf{FCD}}\mathcal{B}$; reloidal product: $latex \mathcal{A}\times^{\mathsf{RLD}}\mathcal{B}$; second product: $latex \mathcal{A}\times^{\mathsf{RLD}}_F\mathcal{B}$; The…
read moreEditing of the article Funcoids and Reloids led to almost ready preprint. I can’t publish it just now because it refers to not yet published article Filters on Posets and Generalizations. Note that I moved some theorems from Funcoids and Reloids to…
read moreI have checked the new version of the article Funcoids and Reloids for errors. I don’t warrant zero errors, but this version should be neat and readable. Now the new version is considered stable and is the main article referred from Algebraic…
read moreI updated the development version of my draft article “Funcoids and Reloids” at my Algebraic General Topology page. The new version of the article benefits adding the following notations for a funcoid $latex f$: $latex \langle f \rangle^{\ast}$ $latex [ f ]^{\ast}$…
read moreI published at my site a new rewritten version of my article “Funcoids and Reloids”. The new version as it was announced defines funcoids and reloids between arbitrary sets instead of old theory of funcoids and reloids on a single fixed set….
read moreFirst, I’m not (yet) an expert in formalized mathematics. I know Isabelle/ZF better, but have only overall view of Isabelle/HOL. Nevertheless I want to tell my opinion on typed (such as HOL) vs. untyped (such as Isabelle/ZF) systems. Slawomir Kolodynski converted me…
read moreI decided to rewrite my theory of funcoids and reloids with funcoids and reloids defined between arbitrary sets instead of current theory which describes funcoids and reloids on a fixed set. That way I will make funcoids and reloids into categories with…
read moreI updated the draft “Orderings of filters in terms of reloids. Extensions of Rudin-Keisler ordering” at this Web page. In the updated version reloids between different sets (I now call them trans-reloids.) are considered in a formal manner, unlike a somehow informal…
read moreI updated the draft “Orderings of filters in terms of reloids. Extensions of Rudin-Keisler ordering” at this Web page. The updated version contains a new theorem (or rather a counter-example) which I proved with the help of Andreas Blass. This version is…
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