Wong\, Yau-Chuen

• Hahn-Banach's Extension Theorem; Banach spaces and Hilbert spaces; operators and some consequences of Hahn-Banach's Extension Theorem; the Uniform Boundedness Theorem and Banach's Open Mapping Theorem; a structure theorem for compact sets in a Banach space; topological injections and topological surjections; vector topologies; separation theorems and Krein-Milman's Theorem; projective topologies and inductive topologies; normed spaces associated with a locally convex space; vector bornologies; initial bornologies and final bornologies; von Neumann bornologies and locally convex topologies determined by convex bornologies; dual pairs and the weak topologies; elementary duality theory; semi-reflexive spaces and ultra-semi-reflexive spaces; some recent results on compact operators and weakly compact operators; precompact seminorms and Schwartz spaces; elementary Riesz - Schauder's theory; an introduction to operator ideals; an aspect of fixed point theory; an inrtoduction to ordered convex spaces.

Wong\, Yau-Chuen

• Hahn-Banach's Extension Theorem; Banach spaces and Hilbert spaces; operators and some consequences of Hahn-Banach's Extension Theorem; the Uniform Boundedness Theorem and Banach's Open Mapping Theorem; a structure theorem for compact sets in a Banach space; topological injections and topological surjections; vector topologies; separation theorems and Krein-Milman's Theorem; projective topologies and inductive topologies; normed spaces associated with a locally convex space; vector bornologies; initial bornologies and final bornologies; von Neumann bornologies and locally convex topologies determined by convex bornologies; dual pairs and the weak topologies; elementary duality theory; semi-reflexive spaces and ultra-semi-reflexive spaces; some recent results on compact operators and weakly compact operators; precompact seminorms and Schwartz spaces; elementary Riesz - Schauder's theory; an introduction to operator ideals; an aspect of fixed point theory; an inrtoduction to ordered convex spaces.