An orientation reversing homeomorphism of the plane with invariant pseudo-arc

An orientation reversing homeomorphism of the plane with invariant pseudo-arc
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 114 (1992), 1145-1149

DOI: https://doi.org/10.1090/S0002-9939-1992-1092915-4

PDF | Request permission

Using the universal cover of the Möbius band, we construct an example as described in the title which answers a question of K. Kuperberg.

References

R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729–742. MR 27144
R. H. Bing, Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43–51. MR 43451, DOI 10.2140/pjm.1951.1.43
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
Krystyna Kuperberg, A lower bound for the number of fixed points of orientation reversing homeomorphisms, The geometry of Hamiltonian systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 22, Springer, New York, 1991, pp. 367–371. MR 1123283, DOI 10.1007/978-1-4613-9725-0_{1}2
Wayne Lewis, Embeddings of the pseudo-arc in $E^{2}$, Pacific J. Math. 93 (1981), no. 1, 115–120. MR 621602, DOI 10.2140/pjm.1981.93.115

The peudo-arc

117

Edwin E. Moise, An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua, Trans. Amer. Math. Soc. 63 (1948), 581–594. MR 25733, DOI 10.1090/S0002-9947-1948-0025733-4
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

Plane indecomposable continua, prime ends, and embeddings of the pseudo-arc

3