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Dimension Theory

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

Abstract

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.

Keywords

Open Neighborhood Complex Space Dimension Theory Open Neighborhood Versus Multiplicative System 
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 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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