Topological characterization of various types of rings of smooth functions
arXiv:1108.5885
Abstract
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative algebra morphism (without requiring continuity) between near-point determined rings of smooth functions is smooth (and hence continuous).
12 pages