Some new minor results

I’ve proved:

$\bigsqcap \langle \mathcal{A} \times^{\mathsf{RLD}} \rangle T = \mathcal{A} \times^{\mathsf{RLD}} \bigsqcap T$ if $\mathcal{A}$ is a filter and $T$ is a set of filters with common base.

$\bigsqcup \left\{ \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B} \hspace{1em} | \hspace{1em} \mathcal{B} \in T \right\} \neq \mathcal{A} \times^{\mathsf{RLD}} \bigsqcup T$ for some filter $T$ and set of filters $T$ (with a common base).

See preprint of my book.