Magma-valued metric spaces
Commutative Algebra
2025-07-28 v3 Group Theory
Rings and Algebras
Abstract
In the second section, we introduce dense unital magmas and show that a near-ring is dense if and only if it has a positive element smaller that unity. In the third section, we discuss magma-valued metric spaces. The density property of the ordered unital magmas and monoids helps us to generalize a couple of classical results related to the convergence and Cauchy property of sequences. The last section is devoted to magma-valued normed groups and some subgroups of the additive group of Cauchy sequences.
Cite
@article{arxiv.2204.06838,
title = {Magma-valued metric spaces},
author = {Peyman Nasehpour},
journal= {arXiv preprint arXiv:2204.06838},
year = {2025}
}
Comments
My original 6-section paper has been split in two. The first part (4 sections) is now accepted in Quasigroups and Related Systems (final peer-reviewed version). The remaining 2 sections will be developed into a second paper soon