41. More generally, every locally compact , almost connected group is the projective limit of a Lie group. 42. In the special case when " R " is the ring of locally compact abelian group. 43. Of particular importance is the C *-algebra of a locally compact group " G ". 44. The special case of invariant measure for second countable locally compact groups had been shown by Haar in 1933. 45. For a locally compact abelian group " G ", every irreducible unitary representation has dimension 1. 46. It follows that a noncompact Tychonoff space admits a minimal compactification if and only if it is locally compact . 47. Indeed, a Hausdorff manifold is a locally compact Hausdorff space, hence it is ( completely ) regular. 48. Locally compact groups which are connected, locally compact groups " G " are ?-compact.49. Locally compact groups which are connected, locally compact groups " G " are ?-compact. 50. In a locally compact , totally disconnected group, every neighbourhood of the identity contains a compact open subgroup.
