Bolzano-Weierstrass theorem


Given any boundedPlanetmathPlanetmathPlanetmathPlanetmath sequence (an) of real numbers, there exists a convergent subsequence (anj).

More generally, any sequence (an) in a compact subset of a metric space has a convergent subsequence.

Title Bolzano-Weierstrass theoremMathworldPlanetmath
Canonical name BolzanoWeierstrassTheorem
Date of creation 2013-03-22 12:22:21
Last modified on 2013-03-22 12:22:21
Owner yark (2760)
Last modified by yark (2760)
Numerical id 10
Author yark (2760)
Entry type Theorem
Classification msc 26A06
Classification msc 40A05
Synonym Bolzano-WeierstraƟ theorem
Related topic ConvergentSequence
Related topic SequentiallyCompact
Related topic AlternateStatementOfBolzanoWeierstrassTheorem