| 1. | A metric space is Lindel�f if and only if it is second-countable.
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| 2. | Every metric space is therefore, in a natural way, a topological space.
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| 3. | A metric space is compact iff it is complete and totally bounded.
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| 4. | Every isometry group of a metric space is a subgroup of isometries.
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| 5. | For example, a metric space can be regarded as an enriched category.
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| 6. | The definition can be generalized to functions that map between metric spaces.
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| 7. | In general, a metric space may have no geodesics, except constant curves.
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| 8. | The space has a metric ( see metric space for details ).
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| 9. | Thus for metric spaces we have : compactness = cauchy-precompactness + completeness.
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| 10. | In a general metric space, however, a Cauchy sequence need not converge.
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