“Funcoids and Reloids” updated
I 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 $latex f$: $latex \langle f \rangle^{\ast}$ $latex [ f ]^{\ast}$ See the article for the meaning of this new notation.
A new raw draft of “Funcoids and Reloids”
I 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. The new version is yet a rough draft and may contain errors or […]
Untyped formalized systems are wrong
First, 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 into his religion of doing formalized math with Isabelle/ZF and answering “yes” to […]
Funcoids and reloids between arbitrary sets
I 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 objects being (small) sets and morphisms being funcoids and reloids. That will make […]
“Orderings of filters in terms of reloids” – a formal approach
I 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 approach in the previous version of this draft. Instead of proving all properties […]
“Orderings of filters in terms of reloids” – draft updated
I 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 yet too rough draft and I hope to finish rewriting it in a […]
A new theorem about funcoids and generalizated filter bases
I proved the following theorem: Theorem If $latex S$ is a generalized filter base then $latex \left\langle f \right\rangle \bigcap{\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} \left\langle\left\langle f \right\rangle \right\rangle S$ for every funcoid $latex f$. The proof (presented in updated version of this online article) is short but not quite trivial. It was originally formulated as […]
A surprisingly hard problem
I am now trying to prove or disprove this innocently looking but somehow surprisingly hard conjecture: Conjecture If $latex S$ is a generalized filter base then $latex \left\langle f \right\rangle \bigcap{\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} \left\langle\left\langle f \right\rangle \right\rangle S$ for every funcoid $latex f$.
Orderings of filters in terms of reloids – in terms of category theory
My draft article “Orderings of filters in terms of reloids. Extensions of Rudin-Keisler ordering” is updated. Read here. Now it uses the language of basic category theory. It is yet not carefully checked for errors.
My motivation to do math research
In the past I considered my purpose to exactly and directly follow commandments of Bible. I had some purposes hardly set as the aim of my life. My life was driven by these purposes not by my wish or my heart. I understood that it was wrong, Bible is more subtle than just a list […]