In the last version of Reloids and Funcoids online article I proved true the following conjecture: Theorem If $latex f$, $latex g$, $latex h$ are reloids then $latex f\circ (g\cup^{\mathsf{RLD}} h) = f\circ g \cup^{\mathsf{RLD}} f\circ h$; $latex (g\cup^{\mathsf{RLD}} h) \circ f…
read moreThe conjecture “Every monovalued reloid is a restricted function” is proved true as a corollary of this theorem in the last revision of Funcoids and Reloids online article.
read moreIn the last revision of Funcoids and Reloids online article I proved that every monovalued reloid with atomic domain is atomic. Consequently two following conjectures are proved true: Conjecture A monovalued reloid restricted to an atomic filter object is atomic or empty….
read moreIn a new edition of Funcoids and Reloids article (section “Some counter-examples”) I wrote a counter-example against this conjecture, upholding that there exists a reloid with atomic domain, which is neither injective nor constant. The conjecture is equivalent to this my MathOverflow…
read moreThough my Funcoids and Reloids article was declared as a preprint candidate, I made a substantial addendum to it: Added definitions of injective, surjective, and bijective morphisms. Added a conjecture about expressing composition of reloids through atomic reloids. Added a conjecture characterizing…
read moreConjecture Every monovalued reloid with atomic domain is either an injective reloid; a restriction of a constant function (or both).
read moreThe 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 $latex f$?
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