The section “Filters on a Set” of the preprint of my math book is rewritten noting the fact that $latex \mathrm{Cor}\, \mathcal{A} = \uparrow^{\mathrm{Base} ( \mathcal{A})} \bigcap \mathcal{A}$.
read moreIn this blog I write mainly about mathematics. But this time I will allow myself to write on some philosophy from biblical Christianity positions. Christ is truth, as it is clear from His own words: (John 14:6) “Jesus said to him, “I…
read moreI have proved that there is a bijection from the set $latex \mathsf{FCD}(A;B)$ to a certain subset of $latex \mathsf{RLD}(A;B)$ (which I call funcoidal reloids). See section (currently numbered 8.4) “Funcoidal reloids” in the preprint of my book.
read moreJust today I’ve got the idea of the below conjecture: Definition I call funcoidal such reloid $latex \nu$ that $latex \mathcal{X} \times^{\mathsf{RLD}} \mathcal{Y} \not\asymp \nu \Rightarrow \\ \exists \mathcal{X}’ \in \mathfrak{F}^{\mathrm{Base} ( \mathcal{X})} \setminus \{ 0 \}, \mathcal{Y}’ \in \mathfrak{F}^{\mathrm{Base} ( \mathcal{Y})}…
read moreIn the march of development of my theory, I have expressed many kinds of spaces (topological, proximity, uniform spaces, etc.) through funcoids and reloids subsuming their properties (such as continuity) for my algebraic operations. Now I have expressed Cauchy spaces (and some…
read moreWhen I first saw topogenous relations at first I thought that my definition of funcoids was plagiarized (for some special case). But then I looked the year of publication. It was 1963, long before discovery of funcoids. Topogenous relations are a trivial…
read moreThis my post is about mathematical logic, but first I will explain the story about people who asked or answer this question. A famous mathematician Timoty Gowers asked this question: What is the difference between direct proofs and proofs by contradiction. We,…
read moreI’ve added to the preprint of my book a new theorem (currently numbered theorem 8.30). The theorem states: Theorem $latex g \circ ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}) \circ f = \langle ( \mathsf{FCD}) f^{- 1} \rangle \mathcal{A} \times^{\mathsf{RLD}} \langle ( \mathsf{FCD}) g \rangle…
read moreI have proved the theorem from Wikipedia that every Cauchy filter is contained in a maximal Cauchy filter (in fact I’ve proved a more general statement). I don’t know the standard proof (and don’t know where to find it), so I’ve devised…
read moreI have rewritten my draft article Products in dagger categories with complete ordered Mor-sets. Now I denote the product of an indexed family $latex X$ of objects as $latex \prod^{(Q)} X$ (instead of old confusing $latex Z’$ and $latex Z”$ notation) and…
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