  The notion of good spectral triple is initiated. We prove firstly that any
regular spectral triple may be embedded in a good spectral triple, so that, in
non-commutative geometry, we can restricts to deal only with good spectral
triples. Given a good spectral triple K=(A,H,D), we prove that A is naturally
endowed with a topology, called the K-topology, making it into an unital
Frechet pre C*-algebra, and that the group Inv(A) of its invertible elements
has a canonical structure of Frechet Lie group of Campbell-Baker-Hausdorff type
open in its Lie algebra A; moreover, for any n>0 one has that K_n=(M_n(A),
H\otimes C^n,D\otimes I_n) is still a good spectral triple. One deduces three
important consequences.
