Major Papers


This major paper is a report on author’s study of some topics on topological vector spaces. We prove a well-known Hahn-Banach theorem and some important consequences, including several separation and extension theorems. We study the weak topology on a topological vector space X and the weak-star topology on the dual space X* of X. We also prove the Banach-Alaoglu theorem. Consequently, we characterize the closed convex hull and the closed linear span for sets in X and X* , identify the dual of a subspace of X with the quotient of its annihilator, and obtain the Goldstine theorem as well as some characterizations of reflexive normed spaces.

Primary Advisor

Zhiguo Hu

Program Reader

Mehdi Monfared

Degree Name

Master of Science


Mathematics and Statistics

Document Type

Major Research Paper

Convocation Year


Included in

Analysis Commons