Fixed points
The last one of the fundamental concepts induced by an action of G on X is
that of fixed points .
A point x ÎX is said to be
fixed under g ÎG if and only if gx=x, and the set of all the
fixed points
of g is indicated by
Xg := {x | gx=x }.
More generally, for any subset S ÍG, we put
XS := {x | " g ÎS : gx=x }.
The particular case XG is called the set of
invariants .
harald.fripertinger@kfunigraz.ac.at,
last changed: August 28, 2001
