MathJax

Saturday, October 11, 2014

Notes on interesting mathematical objects

Banach space
  • A complete linear vector space
Hilbert space
  • A complete inner product space (also a Banach space)
  • Well defined concept of orthogonality or angle
  • Norm induced by the associated inner product

Closed set
  • contains all its limit points
  • complement of an open set
Complete set (M)
  • every Cauchy sequence of points in M has a limit in M
  • there are no points missing (inside or at the boundary)

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