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Given two groups $H$ and $G$ why is it the case that $H \times G$ is closed due to the fact that $G$ and $H$ are closed.

I realise I have answered my question but how does the direct product inherit this? How does it work?

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    Would you care to explain what you mean by closed?2012-06-12
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    Given two element of the product their composition under a binary operator is again in the product of the groups2012-06-12
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    @BenDavidson: You may want to say "closed under products", or just say that multiplication is "an operation" (being an operation on a set already implies that the set is closed under the operation). Because one can talk about topological groups, where "closed" actually means something else.2012-06-12
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    I agree with Arturo that it would be a good idea to say "closed under multiplication" in the question. I actually only clicked on this question because I thought there was a chance it might be about topological groups.2012-06-13
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    You are not alone @TaraB - I was under the same impression...2012-08-14

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