| 21. | For instance, this happens for the Hecke algebra of a locally compact group.
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| 22. | One-point compactification extends this definition to locally compact spaces without base points:
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| 23. | I've never seen Pontryagin duality defined for non-locally compact groups.
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| 24. | These all coincide on spaces that are locally compact ?-compact Hausdorff spaces.
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| 25. | Is continuous when Y ^ X is compact-open and Y locally compact Hausdorff.
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| 26. | Every locally compact Hausdorff space is Tychonoff.
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| 27. | However, there is a straightfoward generalization to Locally Compact Abelian ( LCA ) groups.
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| 28. | The following books have chapters on locally compact abelian groups, duality and Fourier transform.
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| 29. | Namely, if a topological vector space is finite dimensional, it is locally compact.
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| 30. | If the space is locally compact then every open set is measurable for this measure.
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