Difference between revisions of "Every lingering sequence has a convergent subsequence/Statement"

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Revision as of 17:16, 6 December 2015

Statement

Let (X,d) be a metric space, then[1]:

  • (xn)n=1X[(xX ϵ>0[|Bϵ(x)(xn)n=1|=0])((kn)n=1N[(nN[kn<kn+1])(xX[lim

This is just a verbose way of expression the statement that:

References

  1. Jump up Introduction to Topology - Theodore W. Gamelin & Robert Everist Greene