## 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.

## Erroneous theorem became a conjecture

I mistakenly used yet unproved statement that $latex \mathrm{up}\,f$ (taken on the filtrator of funcoids) is a filter for every funcoid $latex f$ in proof of a theorem. So after I found this error I downgrade this theorem to the status of conjecture: Conjecture $latex (\mathsf{FCD}) (\mathsf{RLD})_{\mathrm{out}} f = f$ for every funcoid $latex f$.

## Erroneous lemma corrected

In “Funcoids and Reloids” online draft there was an erroneous lemma: Lemma For every two sets $latex S$ and $latex T$ of binary relations and every set $latex A$ $latex \bigcap {\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} T \Rightarrow \bigcap {\nobreak}^{\mathfrak{F}} \{ \langle F \rangle A | F \in S \} = \bigcap{\nobreak}^{\mathfrak{F}} \{ \left\langle G […]

## Errors in Funcoids and Reloids corrected

I corrected some errors in “Funcoids and Reloids” online draft. The main error was messing $latex \subseteq$ and $latex \supseteq$ in the theorem about continuing a function defined on atomic filter objects till $latex \langle f\rangle$ for a funcoid $latex f$ (currently the Theorem 54 but theorem numbering will be changed in the future). I […]

## False proof of an open problem

I earlier proclaimed that I positively solved this conjecture: Conjecture $latex f\cap^{\mathsf{FCD}} g = f\cap g$ for every binary relations $latex f$ and $latex g$. There were error in my proof and I deleted it. See the draft of Funcoids and Reloids article for details on the current state of the problem.

## Erroneous theorem

I found a counter-example and an error in my proof of this (erroneous) theorem in Funcoids and Reloids article: Let $latex f\in\mathsf{FCD}$. If $latex R$ is a set of co-complete funcoids then $latex f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \left\langle f \circ \right\rangle R$. A counter-example: Let $latex \Delta = \{ (-\epsilon;\epsilon) | […]

## Errors in my draft article “Connectedness of funcoids and reloids”

In my draft article “Connectedness of funcoids and reloids” at Algebraic General Topology site I found several serious errors. Sorry, I will correct these at some time in the future. (I don’t know how much time will take to find correct proofs of the corrected theorems.) Now I just wrote on the site that it […]