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    STUDIA MATHEMATICA - Issue no. 4 / 2020  
         
  Article:   THE SIZE OF SOME VANISHING AND CRITICAL SETS.

Authors:  CORNEL PINTEA.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2020.4.11

Published Online: 2020-11-28
Published Print: 2020-12-20
pp. 651-659

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ABSTRACT: We prove that the vanishing sets of all top forms on a non-orientable manifold are at least 1-dimensional in the general case and at most 1-codimensional in the compact case. We apply these facts to show that the critical sets of some differentiable maps are at least 1-dimensional in the general case and at most 1-codimensional when the source manifold is compact.

Keywords: critical and vanishing sets.
 
         
     
         
         
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