Locally Compact Case
This property is interesting in the case of locally compact topological groups, since locally compact compactly generated topological groups can be approximated by locally compact, separable metric factor groups of G. More precisely, for a sequence
- Un
of open identity neighborhoods, there exists a normal subgroup N contained in the intersection of that sequence, such that
- G/N
is locally compact metric separable (the Kakutani-Kodaira-Montgomery-Zippin theorem).
Read more about this topic: Compactly Generated Group
Famous quotes containing the words locally, compact and/or case:
“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 worst enemy of truth and freedom in our society is the compact majority. Yes, the damned, compact, liberal majority.”
—Henrik Ibsen (1828–1906)
“It was a maxim with Mr. Brass that the habit of paying compliments kept a man’s tongue oiled without any expense; and that, as that useful member ought never to grow rusty or creak in turning on its hinges in the case of a practitioner of the law, in whom it should be always glib and easy, he lost few opportunities of improving himself by the utterance of handsome speeches and eulogistic expressions”
—Charles Dickens (1812–1870)