New conjectures about complete funcoids and reloids
After removing an erroneous theorem I posed two new open problems to take its place: Conjecture If $latex f$ is a complete funcoid and $latex R$ is a set of funcoids then $latex f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \langle f \circ \rangle R$. Conjecture If $latex f$ is a complete reloid and […]
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) | […]
“Funcoids and Reloids” contains “Connectedness”
Now Funcoids and Reloids online article contains the section “Connectedness regarding funcoids and reloids” which previously was in a separate article. In this section there are among definitions and theorems a few open problems.
Errors corrected in article “Connectedness of funcoids and reloids”
I have said that there were several errors in my draft article “Connectedness of funcoids and reloids” at Algebraic General Topology site. I have corrected the errors, but now some of what were erroneous theorems downgraded to the status of conjecture.
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 […]
Filters submitted to Documenta Mathematica journal
I sent my preprint of the article “Filters on Posets and Generalizations” to Bulletin des Sciences Mathématiques math journal but so far received no reply. So I sent it to an other journal, Documenta Mathematica.
On the definition of compact funcoids
[I found that my computations below are erroneous, namely $latex \mathrm{Cor} \langle f^{-1}\rangle \mathcal{F} \neq \langle \mathrm{CoCompl} f^{-1}\rangle \mathcal{F}$ in general (the equality holds when $latex \mathcal{F}$ is a set).]
An erroneos theorem (now a conjecture)
In my Algebraic General Topology series was a flaw in the proof of the following theorem. So I re-labeled it as a conjecture. Conjecture A filter $latex \mathcal{A}$ is connected regarding a reloid $latex f$ iff it is connected regarding the funcoid $latex (\mathrm{FCD})f$. Other theorems in my manuscripts are not affected by this error.
Article sent to an other journal
My submission to Bulletin des Sciences Mathématiques math journal was rejected saying that my article is not in the scope of their journal. This is strange because their Web page says “the Bulletin publishes original articles covering all branches of pure mathematics” and my article indeed is original and belongs to pure mathematics. Nevertheless I […]
Funcoids and Reloids updated – complete reloids
I updated online article “Funcoids and Reloids”. The main feature of this update is new section about complete reloids and completion of reloids (with a bunch of new open problems). Also added some new theorems in the section “Completion of funcoids”.