| 41. | The real numbers are uncountably infinite, whereas the rational numbers are countable.
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| 42. | Any second-countable space is a Lindel�f space, but not conversely.
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| 43. | In some cases, however, the base for a poset is countable.
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| 44. | Conversely a compact metric space is second-countable.
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| 45. | Many " well-behaved " spaces in mathematics are second-countable.
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| 46. | Note that the index set need not be countable.
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| 47. | One can then extend by countable additivity to the full ?-algebra.
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| 48. | Forcing, for example, is often explained in terms of countable models.
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| 49. | The countable chain condition is the & alefsym; 1-chain condition.
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| 50. | Natural numbers work well for representing everyday countable objects.
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