Mazur–Ulam theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 18/02/2019

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SUMMARY
=======
In mathematics, the Mazur–Ulam theorem states that if 
  
    
      
        V
      
    
    {\displaystyle V}
   and 
  
    
      
        W
      
    
    {\displaystyle W}
   are normed spaces over R and the mapping 

  
    
      
        f
        :
        V
        →
        W
      
    
    {\displaystyle f\colon V\to W}
  is a surjective isometry, then 
  
    
      
        f
      
    
    {\displaystyle f}
   is affine.
It is named after Stanisław Mazur and Stanislaw Ulam in response to an issue raised by Stefan Banach.