Summary: It is shown that every locally idempotent (locally -pseudoconvex) Hausdorff algebra with pseudoconvex von Neumann bornology is a regular (respectively, bornological) inductive limit of metrizable locally -(-convex) subalgebras of . In the case where , in addition, is sequentially -complete (sequentially advertibly complete), then every subalgebra is a locally -(-convex) Fréchet algebra (respectively, an advertibly complete metrizable locally -(-convex) algebra) for some . Moreover, for a commutative unital locally -pseudoconvex Hausdorff algebra over with pseudoconvex von Neumann bornology, which at the same time is sequentially -complete and advertibly complete, the statements (a)–(j) of Proposition 3.2 are equivalent.
|46H05||General theory of topological algebras|
|46H20||Structure and classification of topological algebras|