The Cantor Riemannium

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 $\sigma$-compact. We construct an example of Riemannium space: The Cantor Riemannium.