An order theoretic characterization of nested spaces

Smithson, R. E.

doi:10.1090/S0002-9939-1981-0620015-6

An order theoretic characterization of nested spaces
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by R. E. Smithson

Proc. Amer. Math. Soc. 83 (1981), 207-210

DOI: https://doi.org/10.1090/S0002-9939-1981-0620015-6

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Abstract:

A characterization of nested spaces in terms of their order theoretic properties is given. This characterization is analogous to the order theoretic characterization of trees given by L. E. Ward, Jr.

References

On arc smooth continua

2

J. B. Fugate, G. R. Gordh Jr., and Lewis Lum, Arc-smooth continua, Trans. Amer. Math. Soc. 265 (1981), no. 2, 545–561. MR 610965, DOI 10.1090/S0002-9947-1981-0610965-3
T. B. Muenzenberger and R. E. Smithson, The structure of nested spaces, Trans. Amer. Math. Soc. 201 (1975), 57–87. MR 355995, DOI 10.1090/S0002-9947-1975-0355995-1
T. B. Muenzenberger and R. E. Smithson, Mobs and semitrees, J. Austral. Math. Soc. Ser. A 21 (1976), no. 1, 56–63. MR 400180, DOI 10.1017/s1446788700016918
T. B. Muenzenberger and R. E. Smithson, Semilattice structures on dendritic spaces, Topology Proc. 2 (1977), no. 1, 243–260 (1978). MR 540609
T. B. Muenzenberger and R. E. Smithson, Fixed point theorems for acyclic and dendritic spaces, Pacific J. Math. 72 (1977), no. 2, 501–512. MR 454953
Leopoldo Nachbin, Topology and order, Van Nostrand Mathematical Studies, No. 4, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. Translated from the Portuguese by Lulu Bechtolsheim. MR 0219042
Raymond E. Smithson, A note on acyclic continua, Colloq. Math. 19 (1968), 67–71. MR 226601, DOI 10.4064/cm-19-1-67-71
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
R. E. Smithson, A common fixed point theorem for nested spaces, Pacific J. Math. 82 (1979), no. 2, 533–537. MR 551712
L. E. Ward Jr., Partially ordered topological spaces, Proc. Amer. Math. Soc. 5 (1954), 144–161. MR 63016, DOI 10.1090/S0002-9939-1954-0063016-5
L. E. Ward Jr., A note on dendrites and trees, Proc. Amer. Math. Soc. 5 (1954), 992–994. MR 71759, DOI 10.1090/S0002-9939-1954-0071759-2
L. E. Ward Jr., Mobs, trees, and fixed points, Proc. Amer. Math. Soc. 8 (1957), 798–804. MR 97036, DOI 10.1090/S0002-9939-1957-0097036-4
L. E. Ward Jr., Recent developments in dendritic spaces and related topics, Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), Academic Press, New York, 1975, pp. 601–647. MR 0362267
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