English

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.

Keywords

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

R2 v1 2026-06-24T10:47:55.483Z