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…
read moreAfter 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…
read moreI 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…
read moreNow 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.
read moreI 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.
read moreIn 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…
read moreI 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.
read more[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).]
read moreIn 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…
read moreMy 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”…
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