# Local topological algebraicity with algebraic coefficients of analytic sets or functions

## TL;DR

This paper proves that any complex or real analytic set or function germ can be topologically transformed into one defined by polynomial equations with algebraic number coefficients, bridging analytic and algebraic structures.

## Contribution

It establishes a topological equivalence between analytic germs and algebraic polynomial germs with algebraic coefficients, extending algebraic approximation results.

## Key findings

- Analytic germs are topologically equivalent to algebraic polynomial germs.
- Polynomial coefficients can be chosen to be algebraic numbers.
- The result applies to both complex and real analytic sets and functions.

## Abstract

We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.