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Definition of Cn-close

  1. Jun 17, 2012 #1
    I'm reading a paper and have came across the term 'Cn-close' in the sense of a curve being C1-close to a circle for example, but can't find a definition of this term anywhere, and would be grateful if anyone could help.
     
  2. jcsd
  3. Jun 17, 2012 #2

    quasar987

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    This is a reference to the C^n topology, or Whitney topology: http://en.wikipedia.org/wiki/Whitney_topologies

    In your case, to say that " As soon as two curves c1, c2: [0,1] --> R² are C^1-close together, then "blahblah"" means that there exists epsilon >0 such that whenever |c1(t) - c2(t)| < epsilon and |dc1/dt - dc1/dt| < epsilon for all t, then "blah blah" holds.

    A reference is Differential Topology by M Hirsch.
     
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