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