Porton, Victor

Distributivity of outward reloid over composition of funcoids ★★

Author(s): Porton

Conjecture   $ ( \mathsf{\tmop{RLD}})_{\tmop{out}} (g \circ f) = ( \mathsf{\tmop{RLD}})_{\tmop{out}} g \circ ( \mathsf{\tmop{RLD}})_{\tmop{out}} f $ for any composable funcoids $ f $ and $ g $.

Keywords: distributive; distributivity; funcoid; functor; outward reloid; reloid

Funcoid corresponding to inward reloid ★★

Author(s): Porton

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

Keywords: funcoid; inward reloid; reloid

Distributivity of composition over union of reloids ★★

Author(s): Porton

Conjecture   If $ f $, $ g $, $ h $ are reloids then
    \item $ f \circ (g \cup h) = f \circ g \cup f \circ h $; \item $ (g \cup h) \circ f = g \circ f \cup h \circ f $.

Keywords: reloid

Monovalued reloid is a restricted function ★★

Author(s): Porton

Conjecture   If a reloid is monovalued then it is a monovalued function restricted to some filter.

Keywords: monovalued morphism; monovalued reloid; reloid

Intersection of complete funcoids ★★

Author(s): Porton

Conjecture   If $ f $, $ g $ are complete funcoids (generalized closures) then $ f \cap^{\mathsf{\tmop{FCD}}} g $ is a complete funcoid (generalized closure).

Keywords: complete funcoid; funcoid; generalized closure

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