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.
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Famous quotes containing the words limit, point and/or compact:
“Greatness collapses of itself: such limit the gods have set to the growth of prosperous states.”
—Marcus Annaeus Lucan (39–65)
“A set of ideas, a point of view, a frame of reference is in space only an intersection, the state of affairs at some given moment in the consciousness of one man or many men, but in time it has evolving form, virtually organic extension. In time ideas can be thought of as sprouting, growing, maturing, bringing forth seed and dying like plants.”
—John Dos Passos (1896–1970)
“The worst enemy of truth and freedom in our society is the compact majority. Yes, the damned, compact, liberal majority.”
—Henrik Ibsen (1828–1906)