| 41. | Algebraic topology is the study of topologically invariant abstract algebra constructions on topological spaces.
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| 42. | Every metric space is therefore, in a natural way, a topological space.
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| 43. | A topological space is locally metrizable Hausdorff space.
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| 44. | The definitions above are for arbitrary topological spaces.
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| 45. | The same definition applies to any topological space which has a finitely generated homology.
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| 46. | Structure must definitely include topological space as well as the standard abstract algebra notions.
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| 47. | Let be a topological space with a subbasis.
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| 48. | In what follows " X " denotes a locally compact topological space.
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| 49. | This makes S into a functor from the category of topological spaces into itself.
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| 50. | A topological space whose topology can be described by a metric is called metrizable.
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