English

The Cantor Riemannium

Complex Variables 2025-12-18 v3 Differential Geometry General Topology

Abstract

The Riemann surface of a holomorphic germ is the space generated by its Weierstrass analytic continuation. The Riemannium space of a holomorphic germ is the space generated by its Borel monogenic continuation. Riemannium spaces are metric, path connected, Gromov length spaces, not necessarily σ\sigma-compact. We construct an example of Riemannium space: The Cantor Riemannium.

Cite

@article{arxiv.2004.10541,
  title  = {The Cantor Riemannium},
  author = {Ricardo Pérez-Marco},
  journal= {arXiv preprint arXiv:2004.10541},
  year   = {2025}
}

Comments

24 pages, 6 figures. Enlarged historical introduction an minor corrections

R2 v1 2026-06-23T15:01:31.882Z