|Jun17-12, 12:31 PM||#1|
Definition of Cn-close
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.
|Jun17-12, 01:12 PM||#2|
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] --> Rē 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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