I have updated my math book with new (easy but) general theorem similar to this (but in other notation):

Theorem If $\mathfrak{Z}$ is an ideal base, then the set of filters on $\mathfrak{Z}$ is a join-semilattice and the binary join of filters is described by the formula $\mathcal{A}\sqcup\mathcal{B} = \mathcal{A}\cap\mathcal{B}$.

I have updated some other theorems to use this general result and so themselves to become a little more general.

In the course of rewriting my book I found and corrected several small errors.

The latest changes of the book are not yet as thoroughly checked for errors as the rest of the book.