| 31. | The rational numbers are an important example of a space which is not locally compact.
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| 32. | Every nonempty complete metric space or nonempty locally compact Hausdorff space is a Choquet space.
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| 33. | As a locally compact space, the real line can be compactified in several different ways.
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| 34. | The algebra of all continuous functions on a Lie group is a locally compact quantum group.
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| 35. | This is true when " F " is locally compact but false in general.
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| 36. | However, they are locally compact.
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| 37. | In spaces that are not locally compact, this is a necessary but not a sufficient condition.
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| 38. | It was also applied to function spaces on other domains, like locally compact groups and manifolds.
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| 39. | As in the real case, an analog of this theorem is true for locally compact Hausdorff spaces.
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| 40. | It can be extended to the Fourier transform of abstract harmonic analysis defined over locally compact abelian groups.
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