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Possible Duplicate:
Are there more general spaces than Euclidean spaces to have the Heine–Borel property?

By Heine-Borel theorem, a closed and bounded subset of the Euclidean space is compact. If we analyze the proof, the only characteristic of Euclidean space that we need is: every bounded subset is contained in a compact subset. Is there a special name this kind of sets?

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    I think HB and this property are equivalent and hence I'll write an answer.2012-03-11
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    @Alex How can something that asks for a name and that asks you some examples be duplicates?2012-03-11
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    @KannappanSampath The question and answers answer the OP's question fully IMHO.2012-03-11
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    I think OP should clarify if (s)he wants to know the name of those spaces in which every bounded set is contained in a compact set or just a list of Heine Borel spaces! Please respond.2012-03-11

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