Inward motions in connected spaces.
The concept of an A-set(1) is broadened and developed in an arbitrary connected T(1)-space X. Movements of such sets under arbitrary functions and under mildly restricted functions from X 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 where X 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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