In Funcoids and Reloids online article I added two new open problems: 1. $latex \mathrm{Compl} f = f \setminus^{\ast \mathsf{FCD}} (\Omega\times^{\mathsf{FCD}} \mho)$ for every funcoid $latex f$? 2. $latex \mathrm{Compl} f = f \setminus^{\ast \mathsf{RLD}} (\Omega\times^{\mathsf{RLD}} \mho)$ for every reloid $latex f$?

read moreMy online article Funcoids and Reloids as well as my list of open problems are updated. Added two open problems: 1. $latex (\mathsf{RLD})_{\mathrm{in}}$ is not a lower adjoint (in general)? 2. $latex (\mathsf{RLD})_{\mathrm{out}}$ is neither a lower adjoint nor an upper adjoint…

read moreMy online draft article Funcoids and Reloids updated with minor changes in “Connectedness regarding funcoids and reloids” section.

read moreAs I wrote before my preprint Connectors and generalized connectedness was rejected, saying that I do not relate it with existing research. I decided to sent the manuscript to Rejecta Mathematica. I submitted it to Rejecta Mathematica yesterday. Previously I was going…

read moreIn the past I overlooked the following two open problems considering them obvious. When I tried to write proofs of these statements down I noticed these are not trivial. So I added them to my list of open problems. Question $latex (\mathsf{RLD})_{\mathrm{out}}…

read moreExample There exist funcoids $latex {f}&fg=000000$ and $latex {g}&fg=000000$ such that $latex \displaystyle ( \mathsf{RLD})_{\mathrm{out}} (g \circ f) \neq ( \mathsf{RLD})_{\mathrm{out}} g \circ ( \mathsf{RLD})_{\mathrm{out}} f. &fg=000000$ Proof: Take $latex {f = {( =)} |_{\Omega}}&fg=000000$ and $latex {g = \mho \times^{\mathsf{FCD}} \left\{…

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