Communications in Analysis and Geometry

Volume 23 (2015)

Number 2

Topological characterization of various types of $\mathcal{C}^{\infty}$-rings

Pages: 349 – 361

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n2.a5

Author

Dennis Borisov (Mathematisches Institut, Universität Göttingen, Germany)

Abstract

Topologies on algebraic and equational theories are used to define germ determined, near-point determined and point determined $\mathcal{C}^{\infty}$-rings, without requiring them to be finitely generated. It is proved that any $\mathbb{R}$-algebra morphism (without requiring continuity) into a near-point determined $\mathcal{C}^{\infty}$ring is a $\mathcal{C}^{\infty}$ morphism (and hence continuous).

Full Text (PDF format)

Published 17 December 2014