Continuity notions for multi-valued mappings
نویسندگان
چکیده
If we regard a multi-valued mapping as a generalization of a single-valued mapping, we may ask for generalizations of important properties as well, concerning fixed-points, projection, composition etc. The main interest in this paper are continuity notions for multi-valued mappings which allow non-connected images, but still have a certain fixed-point property. The starting point is a continuity notion introduced by the second author in [23], which was stated to possess a zero-property. However, we provide a counterexample to this theorem. Two other continuity notions are introduced and examined, and applied in a logical field.
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