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A nonmetric indecomposable homogeneous continuum every proper subcontinuum of which is an arc. (English) Zbl 0489.54031


MSC:

54F15 Continua and generalizations
54G20 Counterexamples in general topology
54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites
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References:

[1] Haskell Cohen, A cohomological definition of dimension for locally compact Hausdorff spaces, Duke Math. J. 21 (1954), 209 – 224. · Zbl 0058.16605
[2] G. R. Gordh Jr., On homogeneous hereditarily unicoherent continua, Proc. Amer. Math. Soc. 51 (1975), 198 – 202. · Zbl 0277.54034
[3] A. Gutek, A generalization of solenoids, Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978) Colloq. Math. Soc. János Bolyai, vol. 23, North-Holland, Amsterdam-New York, 1980, pp. 547 – 554.
[4] -, Ph. D. Thesis, Uniwersytet Slaski, 1981.
[5] Charles L. Hagopian, A characterization of solenoids, Pacific J. Math. 68 (1977), no. 2, 425 – 435. · Zbl 0364.54027
[6] Anne Lester Hudson and Paul S. Mostert, A finite dimensional homogeneous clan is a group, Ann. of Math. (2) 78 (1963), 41 – 46. · Zbl 0118.03103
[7] J. D. Newburgh, Metrization of finite dimensional groups, Duke. Math. J. 20 (1953), 287 – 293. · Zbl 0051.02001
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