Refluent multifunctions on semitrees

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

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

Refluent multifunctions on semitrees
HTML articles powered by AMS MathViewer

by T. B. Muenzenberger and R. E. Smithson PDF

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

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.

References

David P. Bellamy, Composants of Hausdorff indecomposable continua; a mapping approach, Pacific J. Math. 47 (1973), 303–309. MR 331345
W. Holsztyński, Fixed points of arcwise connected spaces, Fund. Math. 64 (1969), 289–312. MR 248757, DOI 10.4064/fm-64-3-289-312
T. B. Muenzenberger and R. E. Smithson, Fixed point structures, Trans. Amer. Math. Soc. 184 (1973), 153–173 (1974). MR 328900, DOI 10.1090/S0002-9947-1973-0328900-X

Mobs and nested spaces

The structure of semitrees

Fixed points for multi-valued functions on $B$-spaces

R. E. Smithson, Fixed point theorems for certain classes of multifunctions, Proc. Amer. Math. Soc. 31 (1972), 595–600. MR 288750, DOI 10.1090/S0002-9939-1972-0288750-4
L. E. Ward Jr., A fixed point theorem for multi-valued functions, Pacific J. Math. 8 (1958), 921–927. MR 103446
L. E. Ward Jr., Characterization of the fixed point property for a class of set-valued mappings, Fund. Math. 50 (1961/62), 159–164. MR 133122, DOI 10.4064/fm-50-2-159-164
Gail S. Young Jr., The introduction of local connectivity by change of topology, Amer. J. Math. 68 (1946), 479–494. MR 16663, DOI 10.2307/2371828