Compactly Generated Group
In mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. This should not be confused with the unrelated notion (widely used in algebraic topology) of a compactly generated space -- one whose topology is generated (in a suitable sense) by its compact subspaces.
Read more about Compactly Generated Group: Definition, Locally Compact Case
Famous quotes containing the words generated and/or group:
“It is precisely the purpose of the public opinion generated by the press to make the public incapable of judging, to insinuate into it the attitude of someone irresponsible, uninformed.”
—Walter Benjamin (18921940)
“Now, honestly: if a large group of ... demonstrators blocked the entrances to St. Patricks Cathedral every Sunday for years, making it impossible for worshipers to get inside the church without someone escorting them through screaming crowds, wouldnt some judge rule that those protesters could keep protesting, but behind police lines and out of the doorways?”
—Anna Quindlen (b. 1953)