# Intersecting two staroidal products

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

Conjecture. $\prod^{\operatorname{Strd}}a\not\asymp\prod^{\operatorname{Strd}}b% \Leftrightarrow b\in\prod^{\operatorname{Strd}}a\Leftrightarrow a\in\prod^{% \operatorname{Strd}}b\Leftrightarrow\forall i\in n:a_{i}\not\asymp b_{i}$ for every $n$-indexed families $a$ and $b$ of filters on powersets.

The above conjecture has the below consequence (see my book for not so long proof).

Conjecture. Let $f$ is a staroid on powersets and $a\in\prod_{i\in\operatorname{arity}f}\operatorname{Src}f_{i}$, $b\in\prod_{i\in\operatorname{arity}f}\operatorname{Dst}f_{i}$. Then

 $\prod^{\operatorname{Strd}}a\left[\prod^{(C)}f\right]\prod^{\operatorname{Strd% }}b\Leftrightarrow\forall i\in n:a_{i}[f_{i}]b_{i}.$
Title Intersecting two staroidal products IntersectingTwoStaroidalProducts 2013-03-22 19:50:13 2013-03-22 19:50:13 porton (9363) porton (9363) 3 porton (9363) Conjecture msc 54J05 msc 54A05 msc 54D99 msc 54E05 msc 54E17 msc 54E99