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Refluent multifunctions on semitrees


Authors: T. B. Muenzenberger and R. E. Smithson
Journal: Proc. Amer. Math. Soc. 44 (1974), 189-195
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1974-0341462-2
MathSciNet review: 0341462
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Abstract: The concept of refluent on arcs is introduced for multifunctions on semitrees. This notion is then used to obtain a fixed point structure which has as corollaries some generalizations of known fixed point theorems in arcwise connected spaces. For example, we generalize: each continuous point closed multifunction on an arboroid has a fixed point. The final section of the paper develops the relationships between a number of classes of multifunctions on nested spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0341462-2
Keywords: Multifunctions, fixed point structures, dendroids, arboroids, semitrees
Article copyright: © Copyright 1974 American Mathematical Society

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