Graph product of multifuncoids

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Recomm. for undergrads: no
Posted by: porton
on: February 12th, 2012
Conjecture   Let $ F $ is a family of multifuncoids such that each $ F_i $ is of the form $ \lambda j \in N \left( i \right) : \mathfrak{F} \left( U_j \right) $ where $ N \left( i \right) $ is an index set for every $ i $ and $ U_j $ is a set for every $ j $. Let every $ F_i = E^{\ast} f_i $ for some multifuncoid $ f_i $ of the form $ \lambda j \in N \left( i \right) : \mathfrak{P} \left( U_j \right) $ regarding the filtrator $ \left( \prod_{j \in N \left( i \right)} \mathfrak{F} \left( U_j \right) ; \prod_{j \in N \left( i \right)} \mathfrak{P} \left( U_j \right) \right) $. Let $ H $ is a graph-composition of $ F $ (regarding some partition $ G $ and external set $ Z $). Then there exist a multifuncoid $ h $ of the form $ \lambda j \in Z : \mathfrak{P} \left( U_j \right) $ such that $ H = E^{\ast} h $ regarding the filtrator $ \left( \prod_{j \in Z} \mathfrak{F} \left( U_j \right) ; \prod_{j \in Z} \mathfrak{P} \left( U_j \right) \right) $.

See Algebraic General Topology, especially the theory of multifuncoids for definitions of used concepts.


*Victor Porton. Algebraic General Topology

* indicates original appearance(s) of problem.