Compact funcoids – $100 for one who finds my error
I have put online a rough draft of an article about compact funcoids. In the draft article there is an error which I have trouble to find. I will pay $100 to the first person which finds my error (unless I find the error myself). See inside the article.
A section about relationships of different products in my book
I have added new section 16.13 “Relationships of cross-composition and subatomic products” with some important theorems (which I am going to use in the second volume of my book) to my preprint. I have also removed altogether the section “Displaced product” and the definition of displaced product, as it has turned out that displaced product […]
Conjecture solved positively
I’ve proved this conjecture. See my book (which also contains a pointfree version of this theorem).
A conjecture about atomic funcoids
A new conjecture: Conjecture $latex \langle f \rangle \mathcal{X} = \bigsqcup_{F \in \mathrm{atoms}\, f} \langle F \rangle \mathcal{X}$ for every funcoid $latex f$ and $latex \mathcal{X} \in \mathfrak{F} (\mathrm{Src}\, f)$. This conjecture seems important for the notion of exponential object in the category of continuous maps between endofuncoids, which I am investigating now.
The category Fcd has small co-products
Two days ago I have proved that the category Fcd of continuous maps between endofuncoids has small products. Today I have also proved that this category has small co-products. The draft article is now available online. I’m yet to check whether product functors preserve co-products and whether my category has exponential objects and so is […]
The category of continuous maps between endofuncoids has small products
I have proved that Theorem The category of continuous maps between endofuncoids has small products. See my draft article for a proof.
I’ve fixed the error in my proof
I have quickly corrected the error in my proof of an important theorem. Now it is even more beautiful.
Error in my proof
That proof which I claimed in this blog post is with an error: I have messed product of objects and product of morphisms. Now I desperately attempt to repair the proof.
Direct product in the category of continuous maps between endofuncoids
I released a rough draft of my article Direct product in the category of continuous maps between endofuncoids. This (among other) solves the problem I proposed in this blog post. Previously I have said that my research got stuck. Now I see how to continue it! I am again blessed.
Conjecture solved
I’ve published in my book’s preprint a theorem (currently numbered 6.100) which solves a former conjecture. Theorem $latex g \circ \left( \bigsqcup R \right) = \bigsqcup \left\{ g \circ f \,|\, g \in R \right\} = \bigsqcup \langle g \circ \rangle R$ if $latex g$ is a complete funcoid. My shame, I have earlier overlooked […]