I have defined two new kinds of products of funcoids: $latex \prod^{\mathrm{in}}_{i \in \mathrm{dom}\, f} f = \prod^{(C)}_{i \in \mathrm{dom}\, f} (\mathsf{RLD})_{\mathrm{in}} f_i$ (cross-inner product). $latex \prod^{\mathrm{out}}_{i \in \mathrm{dom}\, f} f = \prod^{(C)}_{i \in \mathrm{dom}\, f} (\mathsf{RLD})_{\mathrm{out}} f_i$ (cross-outer product). These products…

read moreI’ve added to my book the following conjecture: Conjecture For every composable funcoids $latex f$ and $latex g$ $latex (\mathsf{RLD})_{\mathrm{out}}(g\circ f)\sqsupseteq (\mathsf{RLD})_{\mathrm{out}}g\circ(\mathsf{RLD})_{\mathrm{out}} f.$

read moreAfter noticing an error in my math book, I rewritten its section “Funcoids and filters” to reflect that $latex (\mathsf{RLD})_\Gamma = (\mathsf{RLD})_{\mathrm{in}}$. Previously I proved an example demonstrating that $latex (\mathsf{RLD})_\Gamma \ne (\mathsf{RLD})_{\mathrm{in}}$, but this example is believed by me to be…

read moreI proved both $latex (\mathsf{RLD})_\Gamma \ne (\mathsf{RLD})_{\mathrm{in}}$ and $latex (\mathsf{RLD})_\Gamma = (\mathsf{RLD})_{\mathrm{in}}$. So there is an error in my math research book. I will post the details of the resolution as soon as I will locate and correct the error. While the…

read moreI claimed earlier that I partially solved this open problem. Today I solved it completely. The proof is available in this PDF file.

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