Extension of $k$-regulous functions from varieties of arbitrary dimension

TL;DR

This paper proves that any $k$-regulous function defined on a non-singular affine variety can be extended to the whole affine space, broadening the understanding of function extension in algebraic geometry.

Contribution

It establishes a general extension theorem for $k$-regulous functions from varieties of any dimension to affine space.

Findings

Extension holds for non-singular affine varieties.

The result applies to varieties of arbitrary dimension.

Provides a foundation for further studies on regulous functions.

Abstract

We prove that a $k$-regulous function defined on a non-singular affine variety can always be extended to the entire affine space.