Certain properties of mininormedspaces

Abstract

In Coding Theory, the Hamming weight defined as the number of non-zero co-ordinates of the code words x satisfies the conditions of a norm except one condition. Instead, it satisfies a new condition. A real valued function satisfying the conditions satisfied by the hamming weight is known as a mininorm. There are many Functions satisfying the conditions of a mininorm. Vector spaces with mininorms are called mininormedspaces. In this paper we discuss certain fundamental properties of mininormedspaces. Linear Maps play a vital role in the theory of vector spaces. We discuss the properties of linear maps between two mininormedspaces. It is established in this paper that, as in normed vector spaces, the continuity of a linear map is determined by its continuity at a Single Point.