### 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
*X*_{g} := {x | gx=x }.

More generally, for any subset *S ÍG*, we put
*X*_{S} := {x | " g ÎS : gx=x }.

The particular case *X*_{G} is called the set of
*invariants* .

harald.fripertinger@kfunigraz.ac.at,

last changed: August 28, 2001