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Completeness

  • Mícheál Ó Searcóid
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

A non-closed subspace of a topological space is singularly defective, particularly if the topology determines geometric structure. We therefore present completeness as a property of universal closure, confining our attention to metric spaces. We shall see that extraordinarily powerful theorems are available in a metric space which contains every possible boundary point in every possible metric superspace.

Keywords

Hilbert Space Banach Space Banach Algebra Cauchy Sequence Division Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2002

Authors and Affiliations

  • Mícheál Ó Searcóid
    • 1
  1. 1.Department of MathematicsUniversity College DublinBelfieldIreland

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