Structural and Topological Properties of Multiplicative Normed Linear Spaces
DOI:
https://doi.org/10.5269/bspm.82350Resumo
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.
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Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
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