I claimed that I have proved the following conjecture: Conjecture $latex \forall H \in \mathrm{up} (g \circ f) \exists F \in \mathrm{up}\, f, G \in \mathrm{up}\, g : H \sqsupseteq G \circ F$ for every composable funcoids $latex f$ and $latex g$….

read moreWARNING: The proof was with an error! I have proved the following theorem: Theorem $latex \forall H \in \mathrm{up} (g \circ f) \exists F \in \mathrm{up}\, f, G \in \mathrm{up}\, g : H \sqsupseteq G \circ F$ for every composable funcoids $latex…

read moreExample There is such a non-symmetric reloid $latex f$ that $latex (\mathsf{FCD})f$ is symmetric. Take $latex f=((\mathsf{RLD})_{\mathrm{in}}(\mathord{=})|_{\mathbb{R}})\sqcap (\mathord{\geq})_{\mathbb{R}}$. I have added this to my online book.

read moreI’ve released my math research book and all supplementary materials free with semicolons replaced with commas to denote tuples: $latex (a;b)$ → $latex (a,b)$, in order to comply with usual math notation of other mathematicians.

read moreCharacterize the set $latex \{f\in\mathsf{FCD} \mid (\mathsf{RLD})_{\mathrm{in}} f=(\mathsf{RLD})_{\mathrm{out}} f\}$. (This seems a difficult problem.)

read moreI have proved $latex (\mathsf{RLD})_{\mathrm{in}} \Omega^{\mathsf{FCD}} = \Omega^{\mathsf{RLD}}$ (where $latex \Omega^{\mathsf{FCD}}$ is a cofinite funcoid and $latex \Omega^{\mathsf{RLD}}$ is a cofinite reloid that is reloid defined by a cofinite filter). The proof is currently available in this draft. Note that in the…

read moreI’ve found a typo in my math book. I confused existential quantifiers with universal quantifiers in the section “Second product. Oblique product” in the chapter “Counter-examples about funcoids and reloids”.

read moreI added more properties of cofinite funcoids to this draft.

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