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It's a basic question, but what do you mean when you say that a group or subgroup is closed? Is this that the action of the group over the corresponding space has always a norm less or equal than some number?

If you could give some examples too, it would be great.

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1 Answer

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Unless you are talking about topology or metric spaces, it usually corresponds to an operator on the group

To be closed under the operator means that if you use the operator on any two elements of the group or subgroup, the result is still contained in the group or subgroup. Note that this closure is required for by the definition of a group.

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