The following is a new conjecture: If $latex f$ and $latex g$ are reloids, then $latex g \circ f = \bigcup{}^{\mathsf{RLD}} \{G \circ F | F \in \mathrm{atoms}^{\mathsf{RLD}} f, G \in \mathrm{atoms}^{\mathsf{RLD}} g \}$.
read moreI updated Funcoids and Reloids article (recently proposed to be the preprint) correcting small errors.
read moreI updated the the online draft of “Funcoids and Reloids” article. This is almost ready preprint (which I will be able to submit after I will have “Filters on Posets and Generalizations” published). The most notable change in this edition is corrected…
read moreIn 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\{…
read moreMy manuscript Connectors and generalized connectedness sent to Topology and its Applications math journal was rejected saying that I have not cited enough articles in order to show that the terminology I introduced and my results are novel, not re-discovery of others’…
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