• 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 Porton11

• 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 Porton16

View the group

• 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 Porton22

View the group

• General Topology
• Generalized path-connectedness in proximity spaces

Let $\delta$ be a proximity.

A set $A$ is connected regarding $\delta$ iff $\forall X,Y \in \mathscr{P} A \setminus \{ \emptyset \} : \left( X \cup Y = A \Rightarrow X \mathrel{\delta} Y \right)$.

Conjecture The following statements are equivalent for every endofuncoid $\mu$ and a set $U$:

- $U$ is connected regarding $\mu$. ...

UnconfirmedYear of origin: 2018

Posted online: 2018-12-01 20:47:59Z by Victor Lvovich Porton17

• General Topology
• 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 $\mathfrak{F} \Gamma$ on the lattice $\Gamma$ of all finite unions of products.

Problem Is $\bigcap^{\mathsf{FCD}}$ a bijection from hyperfuncoids $\mathfrak{F} \Gamma$ to:

- prestaroids on $\mathfrak{A}$;

- staroids on $\mathfrak{A}$; ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:43:06Z by Victor Lvovich Porton12

• General Topology
• 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 sources and destinations. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:39:49Z by Victor Lvovich Porton6

• General Topology
• A funcoid related to directed topological spaces

Conjecture Let $R$ be the complete funcoid corresponding to the usual topology on extended real line $[-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\infty\}$. Let $\geq$ be the order on this set. Then $R\sqcap^{\mathsf{FCD}}\mathord{\geq}$ is a complete funcoid. ...

OpenYear of origin: 2018

Posted online: 2018-12-01 20:38:05Z by Victor Lvovich Porton9

• General Topology
1. 1
2. 2
3. ...
4. 16
5. 17