I'm familiar with the concept of a endomorphism and automorphism, but I don't know it means for them to be continuous... I have tried searching for a defintion online without any success... Any help defining this will be really appreciated!
2026-03-27 15:07:36.1774624056
What is a continuous endomorphism of a group?
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Continuity doesn't make sense on just a group. However, many times you have not only group operations but also a topology on your group. If this topology is such that the group operation and the inverse operation are both continuous, what we have is called a topological group.
Examples of topological groups include $\Bbb R$ with addition and the standard topology, and $S^2$ with rotations and the standard topology.
And once you have a topological group, you can ask whether an automorphism or endomorphism is continuous.