• 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. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 21:10:30Z by Victor Lvovich Porton15

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• General Topology
• 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. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 21:10:30Z by Victor Lvovich Porton11

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• General Topology
• Graph product of multifuncoids

Conjecture Let $F$ is a family of multifuncoids such that each $F_i$ is of the form $\lambda j \in N \left( i \right) : \mathfrak{F} \left( U_j \right)$ where $N \left( i \right)$ is an index set for every $i$ and $U_j$ is a set for every $j$. Let every $F_i = E^{\ast} f_i$ for some multifuncoid $f_i$ of the form $\lambda j \in N \left( i \right) : \mathfrak{P} \left( U_j \right)$ regarding the filtrator $\left( \prod_{j \in N \left( i \right)} \mathfrak{F} \left( U_j \right) ; \prod_{j \in N \left( i \right)} \mathfrak{P} \left( U_j \right) \right)$. Let $H$ is a graph-composition of $F$ (regarding some partition $G$ and external set $Z$). Then there exist a multifuncoid $h$ of the form $\lambda j \in Z : \mathfrak{P} \left( U_j \right)$ such that $H = E^{\ast} h$ regarding the filtrator $\left( \prod_{j \in Z} \mathfrak{F} \left( U_j \right) ; \prod_{j \in Z} \mathfrak{P} \left( U_j \right) \right)$. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 21:01:03Z by Victor Lvovich Porton4

• General Topology
• 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 pointfree funcoid $f_1 \times^{\left( D \right)} f_2$ such that (for every filter $x$ on $A$) $$\left\langle f_1 \times^{\left( D \right)} f_2 \right\rangle x = \bigcup \left\{ \langle f_1\rangle X \times^{\mathsf{FCD}} \langle f_2\rangle X \; | \; X \in \mathrm{atoms}^{\mathfrak{A}} x \right\}.$$ (The join operation is taken on the lattice of filters with reversed order.) ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:59:26Z by Victor Lvovich Porton6

• General Topology
• 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-complete reloid;

- $\operatorname{CoCompl} ( f \circ g) = f \circ \operatorname{CoCompl} g$ if $f$ is a complete reloid; ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:56:15Z by Victor Lvovich Porton7

• General Topology
• Every metamonovalued funcoid is monovalued

Conjecture Every metamonovalued funcoid is monovalued. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:53:47Z by Victor Lvovich Porton10

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• General Topology
• Every metamonovalued reloid is monovalued.

Conjecture Every metamonovalued reloid is monovalued. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:53:47Z by Victor Lvovich Porton16

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• General Topology
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