| 41. | Before 1957 he mainly worked on pure mathematics, specially on topological groups, Lie groups and generalized function theory.
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| 42. | It is known, however, that " local topological groups " do not necessarily have global counterparts.
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| 43. | Since the fundamental group of a topological group is always abelian, every covering group is a normal covering space.
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| 44. | In mathematics, a "'topological group "'is a continuous functions with respect to the topology.
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| 45. | The real numbers, "'R "'with the usual topology form a topological group under addition.
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| 46. | Indeed, analysts may refer to the ordinary, non-topological groups studied by algebraists as " discrete groups ".
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| 47. | By the previous construction the universal cover can be made into a topological group with the covering map a continuous homomorphism.
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| 48. | It is the coarsest topology, emerging from the topology on R, that makes R ^ \ times a topological group.
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| 49. | A principal-bundle, where denotes any topological group, is a fiber bundle together with a Hausdorff and possibly paracompact.
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| 50. | In E . Martin-Peinador, " A reflexible admissible topological group must be locally compact ", Proc.
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