Dimension Theory

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 265)


There are basically three possibilities to introduce the notion of dimension at a point x of a complex space X: topologically as the dimension of the topological space X at x; analytically as the smallest integer n such that n holomorphic functions have x as an isolated zero; and algebraically as the smallest number d of germs f1x ,...,fdx∈m x , such that the ring \({\mathcal{O}_x}/({f_{1x}}, \ldots ,{f_{dx}}){\mathcal{O}_x}\) is artinian.


Open Neighborhood Complex Space Dimension Theory Open Neighborhood Versus Multiplicative System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Mathematisches InstitutUniversität MünsterMünsterGermany

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