Tight Extensions of Normed Spaces

Extensions of Normed Algebras

(Minor corrections and additions have been made. The page layout has also been changed.) 0 Contents Contents 1 Abstract 2 Chapter 1: Constructions and Elementary Properties and Applications of Algebraic Extensions of Normed Algebras 3

Algebraic Extensions of Normed Algebras

Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author's. Acknowledgement: Many thanks to Joel Feinstein for guidance with the literature, useful suggestions and comments on this work.

Normed Gyrolinear Spaces: A Generalization of Normed Spaces Based on Gyrocommutative Gyrogroups

‎In this paper‎, ‎we consider a generalization of the real normed spaces and give some examples‎.  

NORMED HYPERVECTOR SPACES

The main purpose of this paper is to study normed hypervector spaces. We generalize some definitions such as basis, convexity, operator norm, closed set, Cauchy sequences, and continuity in such spaces and prove some theorems about them.

-approximation in normed spaces