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# Intersection with a staroid product through its upper sets

Prerequisites: Algebraic 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.)

Type of Math Object:

Conjecture

Major Section:

Research

## Mathematics Subject Classification

54J05*no label found*54A05

*no label found*54D99

*no label found*54E05

*no label found*54E17

*no label found*54E99

*no label found*

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