Funcoidal products inside an inward reloid
Conjecture (solved) If $a \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} b \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensu...
Upgrading a completary multifuncoid
Let $\mho$ be a set, $\mathfrak{F}$ be the set of filters on $\mho$ ordered reverse to set-theoretic inclusion, $\mathfrak{P}$ be the set of principal...
Atomicity of the poset of completary multifuncoids
Conjecture The poset of completary multifuncoids of the form $(\mathscr{P}\mho)^n$ is for every sets $\mho$ and $n$: - atomic; - atomistic. See belo...
Atomicity of the poset of multifuncoids
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...
Graph product of multifuncoids
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)...
A conjecture about direct product of funcoids
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...
Closing Lemma for Diffeomorphism (Dynamical Systems)
Conjecture Let $f\in Diff^{r}(M)$ and $p\in\omega_{f}$. Then for any neighborhood $V_{f}\subset Diff^{r}(M)$ there is $g\in V_{f}$ such that $p$ is pe...
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)
Conjecture Let $Diff^{r}(M)$ be the space of $C^{r}$ Diffeomorphisms on the connected, compact and boundaryles manifold M and $\chi^{r}(M)$ the space ...
Decomposition of completions of reloids
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...
Every metamonovalued funcoid is monovalued
Conjecture Every metamonovalued funcoid is monovalued. The reverse is almost trivial: Every monovalued funcoid is metamonovalued....
Every metamonovalued reloid is monovalued
Conjecture Every metamonovalued reloid is monovalued....
Generalized path-connectedness in proximity spaces
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 ...
Direct proof of a theorem about compact funcoids
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,...
Another conjecture about reloids and funcoids
Definition $\square f = \bigcap^{\mathsf{RLD}} \mathrm{up}^{\Gamma (\operatorname{Src} f; \operatorname{Dst} f)} f$ for reloid $f$. Conjecture $(\mat...
What are hyperfuncoids isomorphic to?
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...
Infinite distributivity of meet over join for a principal funcoid
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...
A funcoid related to directed topological spaces
Conjecture Let $R$ be the complete funcoid corresponding to the usual topology on extended real line $[-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\in...
Outward reloid of composition vs composition of outward reloids
Conjecture For every composable funcoids $f$ and $g$ $$(\mathsf{RLD})_{\mathrm{out}}(g\circ f)\sqsupseteq(\mathsf{RLD})_{\mathrm{out}}g\circ(\mathsf{R...
A diagram about funcoids and reloids
Define for posets with order $\sqsubseteq$: - $\Phi_{\ast} f = \lambda b \in \mathfrak{B}: \bigcup \{ x \in \mathfrak{A} \mid f x \sqsubseteq b \}$; ...
Which outer reloids are equal to inner ones
Warning: This formulation is vague (not exact). Question Characterize the set $\{f\in\mathsf{FCD} \mid (\mathsf{RLD})_{\mathrm{in}} f=(\mathsf{RLD})_...
Several ways to apply a (multivalued) multiargument function to a family of filters
Problem Let $\mathcal{X}$ be an indexed family of filters on sets. Which of the below items are always pairwise equal? 1. The funcoid corresponding t...
Rendezvous on a line
Problem Two players start at a distance of 2 on an (undirected) line (so, neither player knows the direction of the other) and both move at a maximum ...