| 41. | This theorem can be generalized to any metric space.
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| 42. | Every Euclidean space is also a complete metric space.
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| 43. | There are many completeness as a metric space ).
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| 44. | The term " metric space " comes from Hausdorff.
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| 45. | The most familiar metric space is 3-dimensional Euclidean space.
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| 46. | In metric spaces, one can define Cauchy sequences.
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| 47. | However, the matter is simpler for metric spaces.
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| 48. | This remains true in other complete metric spaces.
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| 49. | Conversely a compact metric space is second-countable.
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| 50. | More generally, all metric spaces are Hausdorff.
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