The pseudo-circle is not homogeneous

The pseudo-circle is not homogeneous
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 148 (1970), 417-428

DOI: https://doi.org/10.1090/S0002-9947-1970-0256362-7

PDF | Request permission

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
R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653–663. MR 43450
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, Embedding circle-like continua in the plane, Canadian J. Math. 14 (1962), 113–128. MR 131865, DOI 10.4153/CJM-1962-009-3
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
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
Lawrence Fearnley, The pseudo-circle is unique, Bull. Amer. Math. Soc. 75 (1969), 398–401. MR 246265, DOI 10.1090/S0002-9904-1969-12193-2
W. T. Ingram, Concerning non-planar circle-like continua, Canadian J. Math. 19 (1967), 242–250. MR 214037, DOI 10.4153/CJM-1967-016-3
J. R. Isbell, Embeddings of inverse limits, Ann. of Math. (2) 70 (1959), 73–84. MR 107221, DOI 10.2307/1969892

On homogeneity

21

F. Burton Jones, Certain homogeneous unicoherent indecomposable continua, Proc. Amer. Math. Soc. 2 (1951), 855–859. MR 45372, DOI 10.1090/S0002-9939-1951-0045372-4
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-contunu est indécomposable

3

Problème

1

Problème

2

Sibe Mardešić and Jack Segal, $\varepsilon$-mappings onto polyhedra, Trans. Amer. Math. Soc. 109 (1963), 146–164. MR 158367, DOI 10.1090/S0002-9947-1963-0158367-X
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
R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
James Ted Rogers Jr., Pseudo-circles and universal circularly chainable continua, Illinois J. Math. 14 (1970), 222–237. MR 264622