Editing Interior algebra (section)

=== Boolean homomorphisms ===
Early research often considered mappings between interior algebras that were homomorphisms of the underlying Boolean algebras but that did not necessarily preserve the interior or closure operator. Such mappings were called '''Boolean homomorphisms'''. (The terms ''closure homomorphism'' or ''topological homomorphism'' were used in the case where these were preserved, but this terminology is now redundant as the standard definition of a homomorphism in [[universal algebra]] requires that it preserves all operations.) Applications involving countably complete interior algebras (in which countable [[meet (order theory)|meet]]s and [[join (order theory)|join]]s always exist, also called ''σ-complete'') typically made use of countably complete Boolean homomorphisms also called '''Boolean σ-homomorphisms'''—these preserve countable meets and joins.