Relative Stone-Weierstrass theorem for mappings between varieties

TL;DR

This paper introduces a new class of real algebraic varieties with strong approximation properties, enabling better understanding of regular mappings and their extensions between varieties.

Contribution

It defines a novel class of varieties characterized by a rationality condition, enhancing approximation capabilities beyond previous classes.

Findings

New class of varieties with strong approximation properties

Enhanced extension results for regular mappings

Better understanding of mappings between algebraic varieties

Abstract

We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to the classes of malleable and quasi-malleable varieties. The approximation property studied here is stronger than those considered before and allows us to deduce non-trivial facts about extensions of regular mappings between varieties.