# Extensions of arc-analytic functions

## TL;DR

This paper proves that arc-analytic semialgebraic functions defined on arc-symmetric sets can be extended to the entire Euclidean space while preserving their arc-analytic and semialgebraic properties.

## Contribution

It establishes the extension property for arc-analytic semialgebraic functions on arc-symmetric sets, advancing the understanding of their structural behavior.

## Key findings

- Extension of arc-analytic semialgebraic functions to ambient space
- Preservation of arc-analytic and semialgebraic properties during extension
- Supports broader applications in real algebraic geometry

## Abstract

We prove that every arc-analytic semialgebraic function on an arc-symmetric set admits an arc-analytic semialgebraic extension to the whole ambient Euclidean space.