Editing Interior algebra (section)

=== Topomorphisms ===
Topomorphisms are another important, and more general, class of [[morphism]]s between interior algebras. A map ''f'' : ''A'' → ''B'' is a topomorphism if and only if ''f'' is a homomorphism between the Boolean algebras underlying ''A'' and ''B'', that also preserves the open and closed elements of ''A''. Hence:
* If ''x'' is open in ''A'', then ''f''(''x'') is open in ''B'';
* If ''x'' is closed in ''A'', then ''f''(''x'') is closed in ''B''.
(Such morphisms have also been called ''stable homomorphisms'' and ''closure algebra semi-homomorphisms''.) Every interior algebra homomorphism is a topomorphism, but not every topomorphism is an interior algebra homomorphism.