# 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 IntersectionWithAStaroidProductThroughItsUpperSets 2013-03-22 19:48:39 2013-03-22 19:48:39 porton (9363) porton (9363) 2 porton (9363) Conjecture msc 54J05 msc 54A05 msc 54D99 msc 54E05 msc 54E17 msc 54E99