diffeomorphism,
n. (Topology) a differentiable mapping that has a differentiable inverse. Two sets are diffeomorphically equivalent if there is a diffeomorphism of one onto the other. For example, the reals and the interval ]0, ∞[ are diffeomorphically equivalent, since the diffeomorphism
f : R |→ ]0, ∞[ : f(x) = ex
has an inverse
g : ]0, ∞[ |→ R : g(x) = logx.
This is a stronger relation than homeomorphism as there are pairs of sets that are homeomorphic but not diffeomorphic.
f : R |→ ]0, ∞[ : f(x) = ex
has an inverse
g : ]0, ∞[ |→ R : g(x) = logx.
This is a stronger relation than homeomorphism as there are pairs of sets that are homeomorphic but not diffeomorphic.