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