### A counter-example for a conjecture

In 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…

### Two new conjectures in “Funcoids and Reloids” article

Though 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…

### Characterization of monovalued reloids with atomic domains

Conjecture Every monovalued reloid with atomic domain is either an injective reloid; a restriction of a constant function (or both).

### Conjecture: Composition of reloids through atomic reloids

The following is a new conjecture: If $latex f$ and $latex g$ are reloids, then $latex g \circ f = \bigcup{}^{\mathsf{RLD}} \{G \circ F | F \in \mathrm{atoms}^{\mathsf{RLD}} f, G \in \mathrm{atoms}^{\mathsf{RLD}} g \}$.

### Funcoids and Reloids updated

I updated Funcoids and Reloids article (recently proposed to be the preprint) correcting small errors.

### Funcoids and Reloids updated

I 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…