Compact Set

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

See also

Bounded Set, Closed Set, Compact Subset

This entry contributed by Brian Jennings

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Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 2, 1991.Kelley, J. L. General Topology. New York: Van Nostrand, 1955.Kreyszig, E. Introductory Functional Analysis with Applications. New York: Wiley, pp. 77-78, 1989.Munkres, J. R. Topology: A First Course, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2000.

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Compact Set

Cite this as:

Jennings, Brian. "Compact Set." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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