# Topological automorphism

From Groupprops

This article gives a basic definition in the following area: topological group theory

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## Definition

Given a topological group, a **topological automorphism** is a bijective map from the topological group to itself that is both:

- A homeomorphism from the topological group to itself, with respect to the topological space structure
- An automorphism from the topological group to itself, with respect to the group structure