| description: |
The properties of topological (not necessarily locally convex) algebras which are needed in K-theory of topological algebras are studied in the present project. The structure of weakly advertive and TQ-algebras, the conditions on a topological algebra under which all maximal ideals are closed and every closed ideal is contained in some closed maximal ideals are investigated. Problems connected with the existence of abstract joint spectrum and the largest joint spectrum in Gelfand-Mazur algebras are consided. Properties of the category of finitely generated projective topological A-modules and similar categories are studied. An analog of Serre-Swan theorem is proved aand Grothendieck groups of seveeral categories (based on topological algebras) are described. |