| 41. | More generally, every locally compact, almost connected group is the projective limit of a Lie group.
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| 42. | In the special case when " R " is the ring of locally compact abelian group.
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| 43. | Of particular importance is the C *-algebra of a locally compact group " G ".
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| 44. | The special case of invariant measure for second countable locally compact groups had been shown by Haar in 1933.
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| 45. | For a locally compact abelian group " G ", every irreducible unitary representation has dimension 1.
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| 46. | It follows that a noncompact Tychonoff space admits a minimal compactification if and only if it is locally compact.
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| 47. | Indeed, a Hausdorff manifold is a locally compact Hausdorff space, hence it is ( completely ) regular.
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| 48. | Locally compact groups which are connected, locally compact groups " G " are ?-compact.
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| 49. | Locally compact groups which are connected, locally compact groups " G " are ?-compact.
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| 50. | In a locally compact, totally disconnected group, every neighbourhood of the identity contains a compact open subgroup.
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