Open Problem Garden

Reloid corresponding to funcoid is between outward and inward reloid ★★

Author(s): Porton

Conjecture For any funcoid $f$ and reloid $g$ having the same source and destination $( \mathsf{\tmop{RLD}})_{\tmop{out}} f \subseteq g \subseteq ( \mathsf{\tmop{RLD}})_{\tmop{in}} f \Leftrightarrow ( \mathsf{\tmop{FCD}}) g = f.$

Keywords: funcoid; inward reloid; outward reloid; reloid

Posted by porton
updated September 2nd, 2007

filter

Distributivity of union of funcoids corresponding to reloids ★★

Author(s): Porton

Conjecture $\bigcup \left\langle ( \mathsf{\tmop{FCD}}) \right\rangle S = ( \mathsf{\tmop{FCD}}) \bigcup S$ if $S\in\mathscr{P}\mathsf{RLD}(A;B)$ is a set of reloids from a set $A$ to a set $B$ .

Keywords: funcoid; infinite distributivity; reloid

Posted by porton
updated September 2nd, 2007

infinite distributivity

Inward reloid corresponding to a funcoid corresponding to convex reloid ★★

Author(s): Porton

Conjecture $( \mathsf{\tmop{RLD}})_{\tmop{in}} ( \mathsf{\tmop{FCD}}) f = f$ for any convex reloid $f$ .

Keywords: convex reloid; funcoid; functor; inward reloid; reloid

Posted by porton
updated September 2nd, 2007

convex reloid

Outward reloid corresponding to a funcoid corresponding to convex reloid ★★

Author(s): Porton

Conjecture $( \mathsf{\tmop{RLD}})_{\tmop{out}} ( \mathsf{\tmop{FCD}}) f = f$ for any convex reloid $f$ .

Keywords: convex reloid; funcoid; functor; outward reloid; reloid

Posted by porton
updated September 2nd, 2007

inward reloid

distributivity

distributive