I uploaded updated version of Filters on Posets and Generalizations article and sent it to Armenian Journal of Mathematics for peer review. The main change in this version is a counter-example to the conjecture, that every weak partition of a filter object…

read moreAre there a known complete classification of filters (or at least ultrafilters)? By complete classification I mean a characterization of every filter by a family of cardinal numbers such that two filters are isomorphic if and only if they have the same…

read moreI updated my online draft of the “Filters on Posets and Generalizations” article, while a former version of it was submitted as a preprint into Armenian Journal of Mathematics. The main new feature of my online draft is the section “Complementive filter…

read moreIn 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 more