Refluent multifunctions on semitrees

Muenzenberger, T. B.; Smithson, R. E.

doi:10.1090/S0002-9939-1974-0341462-2

Refluent multifunctions on semitrees
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by T. B. Muenzenberger and R. E. Smithson

Proc. Amer. Math. Soc. 44 (1974), 189-195

DOI: https://doi.org/10.1090/S0002-9939-1974-0341462-2

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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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