Earlier I claimed that I proved the following theorem: $latex (\mathcal{A}\ltimes\mathcal{B})\sqcap(\mathcal{A}\rtimes\mathcal{B})=\mathcal{A}\times_{F}^{\mathsf{RLD}}\mathcal{B}$ for every filters $latex \mathcal{A}$, $latex \mathcal{B}$ on sets. (Here $latex \ltimes$ and $latex \rtimes$ is what I call oblique products.) Now I have found an error in my proof, so…

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I have a little generalized the following old theorem: $latex (a\sqcap^{\mathfrak{A}}b)^{\ast}=(a\sqcap^{\mathfrak{A}}b)^{+}=a^{\ast}\sqcup^{\mathfrak{A}}b^{\ast}=a^{+}\sqcup^{\mathfrak{A}}b^{+}$. I have also found a new (easy to prove) theorem: $latex (a\sqcup^{\mathfrak{A}}b)^{\ast}=(a\sqcup^{\mathfrak{A}}b)^{+}=a^{\ast}\sqcap^{\mathfrak{A}}b^{\ast}=a^{+}\sqcap^{\mathfrak{A}}b^{+}$. The above formulas hold for filters on a set (and some generalizations). Do these formulas hold also for funcoids?…

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