Open AccessINWARD MOTIONS IN CONNECTED SPACES
Proceedings Of The National Academy Of SciencesPeer ReviewedG. T. Whyburn1969Journals
The concept of anA -set1 is broadened and developed in an arbitrary connectedT 1 -spaceX . Movements of such sets under arbitrary functions and under mildly restricted functions fromX to itself are analyzed. Areas of constricted action are located which are imposed on the function by the structure of the space. Applications are made to the case whereX is a dendrite. In this case existence of points of restricted motion is proved for arbitrary functions which yield actual fixed points in case of partly continuous functions.
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