Locally Compact Abelian Groups
A topological group is locally compact if and only if the identity e of the group has a compact neighborhood. This means that there is some open set V containing e whose closure is compact in the topology of G.
Read more about this topic: Pontryagin Duality
Famous quotes containing the words locally, compact and/or groups:
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“The Puritans, to keep the remembrance of their unity one with another, and of their peaceful compact with the Indians, named their forest settlement CONCORD.”
—Ralph Waldo Emerson (1803–1882)
“And seniors grow tomorrow
From the juniors today,
And even swimming groups can fade,
Games mistresses turn grey.”
—Philip Larkin (1922–1986)