Unsolved Problems

Conjecture The poset of completary multifuncoids of the form $(\mathscr{P}\mho)^n$ is for every sets $\mho$ and $n$: - atomic; - atomistic. See belo...

Conjecture The poset of multifuncoids of the form $(\mathscr{P}\mho)^n$ is for every sets $\mho$ and $n$: - atomic; - atomistic. See below for defin...

Conjecture Let $F$ is a family of multifuncoids such that each $F_i$ is of the form $\lambda j \in N \left( i \right): \mathfrak{F} \left( U_j \right)...

Conjecture Let $f_1$ and $f_2$ are monovalued, entirely defined funcoids with $\operatorname{Src}f_1=\operatorname{Src}f_2=A$. Then there exists a poi...

Conjecture For composable reloids $f$ and $g$ it holds - $\operatorname{Compl} ( g \circ f) = ( \operatorname{Compl} g) \circ f$ if $f$ is a co-compl...

Conjecture Every metamonovalued funcoid is monovalued. The reverse is almost trivial: Every monovalued funcoid is metamonovalued....

Conjecture Every metamonovalued reloid is monovalued....

Let $\delta$ be a proximity. A set $A$ is connected regarding $\delta$ iff $\forall X,Y \in \mathscr{P} A \setminus \{ \emptyset \}: \left( X \cup Y ...

Conjecture Let $f$ is a $T_1$-separable (the same as $T_2$ for symmetric transitive) compact funcoid and $g$ is a uniform space (reflexive, symmetric,...

Definition $\square f = \bigcap^{\mathsf{RLD}} \mathrm{up}^{\Gamma (\operatorname{Src} f; \operatorname{Dst} f)} f$ for reloid $f$. Conjecture $(\mat...

Let $\mathfrak{A}$ be an indexed family of sets. Products are $\prod A$ for $A \in \prod \mathfrak{A}$. Hyperfuncoids are filters $\mathfrak{F} \Gam...

Conjecture $f \sqcap \bigsqcup S = \bigsqcup \langle f \sqcap \rangle^{\ast} S$ for principal funcoid $f$ and a set $S$ of funcoids of appropriate sou...

Conjecture Let $R$ be the complete funcoid corresponding to the usual topology on extended real line $[-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\in...

Conjecture For every composable funcoids $f$ and $g$ $$(\mathsf{RLD})_{\mathrm{out}}(g\circ f)\sqsupseteq(\mathsf{RLD})_{\mathrm{out}}g\circ(\mathsf{R...

Define for posets with order $\sqsubseteq$: - $\Phi_{\ast} f = \lambda b \in \mathfrak{B}: \bigcup \{ x \in \mathfrak{A} \mid f x \sqsubseteq b \}$; ...

Warning: This formulation is vague (not exact). Question Characterize the set $\{f\in\mathsf{FCD} \mid (\mathsf{RLD})_{\mathrm{in}} f=(\mathsf{RLD})_...