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 ?
It follows from the Bolzano-Weierstrass theorem and the closeness of B that there exists [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] such that
Now the sequence ([P.sub.k]) contained in C has, using Bolzano-Weierstrass theorem, a subsequence ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) converging to some [P.sup.*] [member of] C.
Cauchy or sequential compactness, the Bolzano-Weierstrass theorem, etc.).