Structural and Topological Properties of Multiplicative Normed Linear Spaces

Résumé

The primary objective of this research is to formulate a robust topological structure for Multi
plicativeNormed Linear Spaces (MNLS). By re-examining fundamental analytical concepts through a multi
plicative lens, we establish Key theoretical contributions include a characterization of multiplicative closed sets
via limit points and the derivation of a multiplicative version of the Cantor Intersection Principle.We further
demonstrate that finite-dimensional MNLS are inherently complete and that the Heine-Borelproperty holds,
meaning a subspace is compact if and only if it is multiplicatively closed and bounded. Additionally, the study
confirms that continuous mappings on compact domains are necessarily uniformly continuous. These results
provide the essential theoretical scaffolding required for future developments in non-Newtonian calculus and
fixed-point theory.