A distributive law for filter objects
I recently proved the following conjecture (now a theorem): Theorem $latex A\cap^{\mathfrak{F}}\bigcup{}^{\mathfrak{F}}S = \bigcup{}^{\mathfrak{F}} \{ A\cap^{\mathfrak{F}} X | X\in S \}$ for every set $latex A\in\mathscr{P}\mho$ and every $latex S\in\mathscr{P}\mathfrak{F}$ where $latex \mathfrak{F}$ is the set of filter objects on some set $latex \mho$. This theorem is a direct consequence of the following lemma: Lemma […]
A theorem generalized
I generalized a theorem in the preprint article “Filters on posets and generalizations” on my Algebraic General Topology site. The new theorem is formulated as following: Theorem If $latex (\mathfrak{A}; \mathfrak{Z})$ is a join-closed filtrator and $latex \mathfrak{A}$ is a meet-semilattice and $latex \mathfrak{Z}$ is a complete lattice, then $latex \mathrm{Cor}’ (a \cap^{\mathfrak{A}} b) = […]
Filters article sent to Moscow Mathematical Journal
My second submit to Documenta Mathematica journal of “Filters on Posets and Generalizations” preprint was unanswered in reasonable amount of time. As such I submitted it to an other journal, Moscow Mathematical Journal.
Resubmit to Documenta Mathematica
I submitted the preprint of my article “Filters on Posets and Generalizations” to Documenta Mathematica math journal but so far received no reply. So I sent submission to an other editor of the same journal.
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.
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 […]
Conjecture solved and submitted to a journal
First, I solved this conjecture and updated the preprint about filters adding new section “Fréchet filter” which contains the proof of the above mentioned conjecture. Second I submitted this preprint to Bulletin des Sciences Mathématiques math journal via email to the secretary. I have earlier submitted it to the journal editor V.I. Arnold but he […]