A study on completely equivalent generalized normed spaces

Abstract

According to intuition, two spaces $X$  and $Y$   are equivalent if they may be bent, shrunk, or expanded into one another. Spaces that are homotopy-equivalent to a point are called contractible. A vector space can be equipped with more than one norm. In this paper, the necessary and sufficient conditions for n-norms to be completely equivalent on linear $n$ -Banach spaces are obtained.