In mathematics, a topological space X is said to be limit point compact or weakly countably compact if every infinite subset of X has a limit point in X. This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent.
Read more about Limit Point Compact: Properties and Examples
Famous quotes containing the words limit, point and/or compact:
“There is no limit to what a man can do so long as he does not care a straw who gets the credit for it.”
—C.E. (Charles Edward)
“There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.”
—A.J. (Alfred Jules)
“The worst enemy of truth and freedom in our society is the compact majority. Yes, the damned, compact, liberal majority.”
—Henrik Ibsen (1828–1906)