Homogeneous circlelike continua

Lewis, Wayne

doi:10.1090/S0002-9939-1983-0706533-2

Homogeneous circlelike continua
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Proc. Amer. Math. Soc. 89 (1983), 163-168 Request permission

Abstract:

We extend earlier work of Bing, Jones, Hagopian, and Rogers to give a complete classification of nondegenerate homogeneous circle-like continua as pseudo-arcs, solenoids, or solenoids of pseudo-arcs. by showing that solenoids of pseudo-arcs are unique.

References

R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729–742. MR 27144
R. H. Bing, Each homogeneous nondegenerate chainable continuum is a pseudo-arc, Proc. Amer. Math. Soc. 10 (1959), 345–346. MR 105072, DOI 10.1090/S0002-9939-1959-0105072-6
R. H. Bing, A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Canadian J. Math. 12 (1960), 209–230. MR 111001, DOI 10.4153/CJM-1960-018-x
R. H. Bing and F. B. Jones, Another homogeneous plane continuum, Trans. Amer. Math. Soc. 90 (1959), 171–192. MR 100823, DOI 10.1090/S0002-9947-1959-0100823-3
C. E. Burgess, A characterization of homogeneous plane continua that are circularly chainable, Bull. Amer. Math. Soc. 75 (1969), 1354–1356. MR 247611, DOI 10.1090/S0002-9904-1969-12421-3

Ueber topologish homogene kontinua

15

Lawrence Fearnley, The pseudo-circle is not homogeneous, Bull. Amer. Math. Soc. 75 (1969), 554–558. MR 242126, DOI 10.1090/S0002-9904-1969-12241-X
Charles L. Hagopian, Homogeneous circle-like continua that contain pseudo-arcs, Topology Proceedings, Vol. I (Conf., Auburn Univ., Auburn, Ala., 1976) Math. Dept., Auburn Univ., Auburn, Ala., 1977, pp. 29–32. MR 0458380
Charles L. Hagopian, A characterization of solenoids, Pacific J. Math. 68 (1977), no. 2, 425–435. MR 458381, DOI 10.2140/pjm.1977.68.425

Atriodic homogeneous continua

Charles L. Hagopian and James T. Rogers Jr., A classification of homogeneous, circle-like continua, Houston J. Math. 3 (1977), no. 4, 471–474. MR 464194
F. Burton Jones, On a certain type of homogeneous plane continuum, Proc. Amer. Math. Soc. 6 (1955), 735–740. MR 71761, DOI 10.1090/S0002-9939-1955-0071761-1

Un continu dont tout sous-continu est indécomposable

3

Edwin E. Moise, A note on the pseudo-arc, Trans. Amer. Math. Soc. 67 (1949), 57–58. MR 33023, DOI 10.1090/S0002-9947-1949-0033023-X
James T. Rogers Jr., The pseudo-circle is not homogeneous, Trans. Amer. Math. Soc. 148 (1970), 417–428. MR 256362, DOI 10.1090/S0002-9947-1970-0256362-7
James T. Rogers Jr., Solenoids of pseudo-arcs, Houston J. Math. 3 (1977), no. 4, 531–537. MR 464193
James T. Rogers Jr., Almost everything you wanted to know about homogeneous, circle-like continua, Topology Proc. 3 (1978), no. 1, 169–174 (1979). MR 540487