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

harald.fripertinger "at" uni-graz.at | http://www-ang.kfunigraz.ac.at/~fripert/ |

UNI-Graz | Institut für Mathematik |

UNI-Bayreuth | Lehrstuhl II für Mathematik |

Fixed points |