![](/files/happy5.png)
Graph product of multifuncoids
Conjecture Let
is a family of multifuncoids such that each
is of the form
where
is an index set for every
and
is a set for every
. Let every
for some multifuncoid
of the form
regarding the filtrator
. Let
is a graph-composition of
(regarding some partition
and external set
). Then there exist a multifuncoid
of the form
such that
regarding the filtrator
.
![$ F $](/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png)
![$ F_i $](/files/tex/468bb283d323c2779688c7954a9de964d909524f.png)
![$ \lambda j \in N \left( i \right) : \mathfrak{F} \left( U_j \right) $](/files/tex/ec2677105f186d63c73702433a4fe09bcc1e92bc.png)
![$ N \left( i \right) $](/files/tex/ccbc2dd2c65699e06cafe73a1ded06b193ab52f0.png)
![$ i $](/files/tex/ca49c241ece07915c97a31774a977841c6f0414c.png)
![$ U_j $](/files/tex/246b680371106f172aa027bc2c18e977aa2c779b.png)
![$ j $](/files/tex/282a1b4a166eb4c8018038a9ca0d509b2c90b79b.png)
![$ F_i = E^{\ast} f_i $](/files/tex/2e6c4a540867fd2ef352ea31f20e7d00c81d8b07.png)
![$ f_i $](/files/tex/3d8d4274a2a88f65b70123aab5f541cbfb114eb2.png)
![$ \lambda j \in N \left( i \right) : \mathfrak{P} \left( U_j \right) $](/files/tex/0154473bda09e018c819cbf7c181386972c20d4a.png)
![$ \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) $](/files/tex/3be7158866e88b56c057bdb5d058cd619d47bdd4.png)
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ F $](/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ Z $](/files/tex/b85ee8eb04b7b36a6f05b7f6218bef305019f707.png)
![$ h $](/files/tex/cc23d2b0c281befd62457dcbedbf9385be2cd2f6.png)
![$ \lambda j \in Z : \mathfrak{P} \left( U_j \right) $](/files/tex/df5585afb153a7713c3b972518a8808361951cf0.png)
![$ H = E^{\ast} h $](/files/tex/58f97b913328b408982a64ecf4dd15fda6ad2df8.png)
![$ \left( \prod_{j \in Z} \mathfrak{F} \left( U_j \right) ; \prod_{j \in Z} \mathfrak{P} \left( U_j \right) \right) $](/files/tex/5a6d012c147b71bceeaa2eb8bf011efb3caa8ca5.png)
See Algebraic General Topology, especially the theory of multifuncoids for definitions of used concepts.
Bibliography
*Victor Porton. Algebraic General Topology
* indicates original appearance(s) of problem.