Open problems in Mathematics stemming from research papers

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; ...
- Victor Porton
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. ...
- Victor Porton
OpenYear of origin: 2018
Posted online: 2018-12-01 20:53:47Z by Victor Lvovich Porton16

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- General Topology
Every metamonovalued reloid is monovalued.

Conjecture Every metamonovalued reloid is monovalued. ...
- Victor Porton
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 $. ...
- Victor Porton
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 $\mathfrak{A}$; ...
- Victor Porton
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. ...
- Victor Porton
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. ...
- Victor Porton
OpenYear of origin: 2018
Posted online: 2018-12-01 20:38:05Z by Victor Lvovich Porton9
- General Topology

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