| 11. | :So you learn general topology first and then specialize into metric spaces.
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| 12. | Equivalently, in the case of a metric space, this can be expressed as
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| 13. | In fact, the Heine Borel theorem for arbitrary metric spaces reads:
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| 14. | The proof of the generalized theorem to metric space is similar.
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| 15. | For a function between metric spaces, uniform continuity implies Cauchy continuity.
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| 16. | Every compact metric space is complete, though complete spaces need not be compact.
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| 17. | Every metric space has a unique ( up to isometry ) dense subset.
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| 18. | Menger curvature may also be defined on a general metric space.
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| 19. | Includes such notions as convergence, separation axioms, metric spaces, dimension theory.
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| 20. | The unit interval is a complete metric space, locally path connected.
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