Hahn-Banach Extension Theorems
Hsien-Chung Wu · 2025
Chapter 5 studies the Hahn-Banach extension theorem, which is an important theorem in functional analysis based on (conventional) vector space. This chapter tries to establish the Hahn-Banach extension theorems in near vector space and near normed space. Since the (conventional) vector space is a special kind of near vector space and the (conventional) normed space is also a special kind of near normed space, the Hahn-Banach extension theorems established in this chapter cover the (conventional) Hahn-Banach extension theorem in (conventional) vector space. On the other hand, the geometric form of Hahn-Banach extension theorem is very useful in nonlinear analysis, especially in vector optimization problems. Therefore, the geometric form of Hahn-Banach extension theorem in near vector space is also studied for the purpose of providing possible applications in nonlinear analysis.