# filter products

## Strict inequalities for products of filters ★

Author(s): Porton

\begin{conjecture} $\mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} \subset \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B}$ for some filter objects $\mathcal{A}$, $\mathcal{B}$. Particularly, is this formula true for $\mathcal{A} = \mathcal{B} = \Delta \cap \uparrow^{\mathbb{R}} \left( 0 ; + \infty \right)$? \end{conjecture}

A weaker conjecture:

\begin{conjecture} $\mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B}$ for some filter objects $\mathcal{A}$, $\mathcal{B}$. \end{conjecture}

Keywords: filter products