| 1. | Locally compact quantum groups generalize Hopf algebras and carry a topology.
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| 2. | The theorem also holds more generally in locally compact abelian groups.
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| 3. | This gives a Haar measures on a locally compact Hausdorff group.
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| 4. | Being locally compact Hausdorff spaces, manifolds are necessarily Tychonoff spaces.
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| 5. | The locally compact abelian case is part of the Pontryagin duality theory.
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| 6. | In the general locally compact setting, such techniques need not hold.
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| 7. | Let " X " be a locally compact Hausdorff space.
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| 8. | If the topological space is locally compact, these notions are equivalent.
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| 9. | For locally compact spaces an integration theory is then recovered.
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| 10. | Let G be a locally compact, abelian group.
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