Open Problem Garden

Author(s): Porton

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

Keywords: outward reloid

Posted by porton
updated September 10th, 2016

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Topology

A funcoid related to directed topological spaces ★★

Author(s): Porton

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.

Proposition It is easy to prove that $\langle R\sqcap^{\mathsf{FCD}}\mathord{\geq}\rangle \{x\}$ is the infinitely small right neighborhood filter of point $x\in[-\infty,+\infty]$ .

If proved true, the conjecture then can be generalized to a wider class of posets.

Keywords:

Posted by porton
updated July 28th, 2016

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Topology

Infinite distributivity of meet over join for a principal funcoid ★★

Author(s): Porton

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.

Keywords: distributivity; principal funcoid

Posted by porton
updated July 27th, 2016

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principal funcoid

fucnoids

Topology

Entourages of a composition of funcoids ★★

Author(s): Porton

Conjecture $\forall H \in \operatorname{up} (g \circ f) \exists F \in \operatorname{up} f, G \in \operatorname{up} g : H \sqsupseteq G \circ F$ for every composable funcoids $f$ and $g$ .

Keywords: composition of funcoids; funcoids

Posted by porton
updated July 12th, 2016

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