| 11. | The representation theory for locally compact abelian groups is described by Pontryagin duality.
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| 12. | A discrete topological space is locally compact and Hausdorff.
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| 13. | In 1961, Kats extended this result to arbitrary locally compact topological groups.
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| 14. | Let G be a second countable locally compact group.
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| 15. | For locally compact groups, invariance is achievable within certain range of transformations.
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| 16. | Proper spaces are locally compact, but the converse is not true in general.
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| 17. | The irreducible unitary representations of a locally compact group may be infinite-dimensional.
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| 18. | However unlike this field is not locally compact.
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| 19. | In what follows " X " denotes a locally compact topological space.
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| 20. | The real line \ mathbf { R } is a locally compact abelian group.
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