Intersection with a staroid product through its upper sets

Prerequisites: \hrefhttp://www.mathematics21.org/algebraic-general-topology.htmlAlgebraic General Topology.

Conjecture. Let $\mathfrak{F}$ is a family of sets of filters on distributive lattices with least elements. Let $a\in\prod\mathfrak{F}$ , $S\in\mathscr{P}\prod\mathfrak{F}$ is a generalized filter base, $\bigsqcup S=a$ , $f$ is a staroid of the form $\prod\mathfrak{F}$ . Then

\prod^{\operatorname{Strd}(\mathfrak{F})}a\not\asymp f\Leftrightarrow\forall A% \in S:\prod^{\operatorname{Strd}(\mathfrak{A})}A\not\asymp f.

(This conjecture may be weakened for the special case of filters on powersets.)

Title	Intersection with a staroid product through its upper sets
Canonical name	IntersectionWithAStaroidProductThroughItsUpperSets
Date of creation	2013-03-22 19:48:39
Last modified on	2013-03-22 19:48:39
Owner	porton (9363)
Last modified by	porton (9363)
Numerical id	2
Author	porton (9363)
Entry type	Conjecture
Classification	msc 54J05
Classification	msc 54A05
Classification	msc 54D99
Classification	msc 54E05
Classification	msc 54E17
Classification	msc 54E99