MATH 653 Topological Vector Spaces
Vector space topologies, metrizability, locally convex topological vector spaces, Hahn-Banach theorem, projective and inductive topologies, barreled and bornological spaces. Linear mappings, Banach's homomorphism theorem, uniform boundedness and the Banach-Steinhaus theorem, duality, dual systems and weak topologies; strong dual, bi-dual, and reflexive spaces; theorems of Grothendieck, weak compactness, open mappings, and closed graph theorems; linear manifolds and applications. Prerequisites: 620 and 625 .