Bolzano-Weierstrass theorem

Bolzano-Weierstrass theorem

[‚bōl′tsän·ō ′vī·ər‚shträs ‚thir·əm]
(mathematics)
The theorem that every bounded, infinite set in finite dimensional Euclidean space has a cluster point.
References in periodicals archive ?
k]) contained in C has, using Bolzano-Weierstrass theorem, a subsequence ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) converging to some [P.
Cauchy or sequential compactness, the Bolzano-Weierstrass theorem, etc.
This whole subtheory is non-constructive, depending repeatedly on the Bolzano-Weierstrass theorem or, equivalently, sequential compactness.