Chief factors in Polish groups

Abstract In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of for Polish groups. development this we prove version Schreier refinement theorem. also trichotomy topologically characteristically simple The requires two independently interesting lines study. First consider injective, continuous homomorphisms with dense normal image. show such maps admit canonical factorisation via semidirect product, as consequence, these preserve topological simplicity up to abelian error. then define generalisations direct products use isolate notion semisimplicity