Home » Keyword index

distributivity


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
add new comment
Topology

Distributivity of a lattice of funcoids is not provable without axiom of choice ★

Author(s): Porton

Conjecture   Distributivity of the lattice $ \mathsf{FCD}(A;B) $ of funcoids (for arbitrary sets $ A $ and $ B $) is not provable in ZF (without axiom of choice).

A similar conjecture:

Conjecture   $ a\setminus^{\ast} b = a\#b $ for arbitrary filters $ a $ and $ b $ on a powerset cannot be proved in ZF (without axiom of choice).

Keywords: axiom of choice; distributive lattice; distributivity; funcoid; reverse math; reverse mathematics; ZF; ZFC

Posted by porton
updated August 24th, 2013
add new comment
Topology

Distributivity of inward reloid over composition of funcoids ★★

Author(s): Porton

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

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

Posted by porton
updated December 31st, 2011
add new comment
Topology

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

Posted by porton
updated September 2nd, 2007
1 comment
Syndicate content