Bolzano-Weierstrass theorem | Article about Bolzano-Weierstrass theorem by The Free Dictionary
Bolzano-Weierstrass theorem[‚bōl′tsän·ō ′vī·ər‚shträs ‚thir·əm]
The theorem that every bounded, infinite set in finite dimensional Euclidean space has a cluster point.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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