Definition of Cn-close

Ad123q

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.

quasar987

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.