"Generalized 2-Norms on Menger Linear Spaces over Menger Fields: A Comprehensive Study"

Abstract

This article introduces a generalization of the concept of a 2-norm on Menger spaces over Menger fields, extending foundational principles of norm theory to these algebraic structures. The study outlines fundamental axioms governing the 2-norm in this context, establishing a framework for analysing vector magnitudes and distances within Menger spaces. By adapting notions from functional analysis and linear algebra to the setting of Menger spaces and fields, the research seeks to deepen understanding of geometric properties and algebraic structures in these generalized spaces. The exploration of 2-norms in Menger settings offers insights into the interplay between metric properties and algebraic structures, paving the way for further developments in mathematical theory and applications within this framework.