# Uniform Continuity in Definable Groups

## TL;DR

This paper explores analogues of amenability in definable groups, establishing fixed point theorems and proposing new definitions for definable actions and continuous functions, potentially impacting broader mathematical contexts.

## Contribution

It introduces novel definitions for definable actions and continuous functions in the setting of definable groups, along with fixed point theorems, advancing the understanding of amenability analogues.

## Key findings

- Fixed point theorems for definable groups
- New definitions for definable actions and continuous functions
- Potential applications in other mathematical contexts

## Abstract

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous functions from definable groups to topological spaces which might prove useful in other contexts.