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On the absence of tame disks in certain wild cells

Part of the Lecture Notes in Mathematics book series (LNM,volume 438)

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  • Flat Embedding
  • Wild Cell
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References

  1. J. W. Alexander, Remarks on a point set constructed by Antoine, Proc. Nat. Acad. Sci. 10 (1924), pp. 10–12.

    CrossRef  Google Scholar 

  2. L. Antoine, Sur l’homeomorphie de deux figures et de leur voisinages, J. Math. Pures Appl. 4 (1921), pp. 221–325.

    MATH  Google Scholar 

  3. R. H. Bing, Each disk in E 3 contains a tame arc, Amer. J. Math. 84 (1962), pp. 583–590.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. _____, Pushing a 2-sphere into its complement, Michigan Math. J. 11 (1964), pp. 33–45.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. W. A. Blankenship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), pp. 276–291.

    CrossRef  MathSciNet  Google Scholar 

  6. J. L. Bryant, R. D. Edwards, and C. L. Seebeck, III, Approximating codimension one submanifolds with locally homotopically unknotted embeddings, in preparation.

    Google Scholar 

  7. R. J. Daverman, On the scarcity of tame disks in certain wild cells, Fund. Math. 79 (1973), pp. 63–77.

    MathSciNet  MATH  Google Scholar 

  8. ________, Pushing an (n−1)-sphere in S n almost into its complement, Duke Math. J. 39 (1972), pp. 719–723.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. ________, Approximating polyhedra in codimension one spheres embedded in S n by tame polyhedra, Pacific J. Math., to appear.

    Google Scholar 

  10. ________, On cells in E n that cannot be squeezed, Rocky Mtn. J. Math., to appear.

    Google Scholar 

  11. R. J. Daverman and W. T. Eaton, An equivalence for the embeddings of cells in a 3-manifold, Trans. Amer. Math. Soc. 145 (1969), pp. 369–382.

    MathSciNet  MATH  Google Scholar 

  12. R. J. Daverman and R. D. Edwards, in preparation.

    Google Scholar 

  13. J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.

    MATH  Google Scholar 

  14. W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, Princeton, N. J., 1948.

    MATH  Google Scholar 

  15. R. T. Miller, Approximating codimension three embeddings, Ann. of Math. (2) 95 (1972), pp. 406–416.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. R. P. Osborne, Embedding Cantor sets in a manifold. II. An extension theorem for homeomorphisms on Cantor sets, Fund. Math. 65 (1969), pp. 147–151.

    MathSciNet  MATH  Google Scholar 

  17. C. L. Seebeck, III, Tame arcs on wild cells, Proc. Amer. Math. Soc. 29 (1971), pp. 197–201.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. R. B. Sher, Tame polyhedra in wild cells and spheres, Proc. Amer. Math. Soc. 30 (1971), pp. 169–174.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1975 Springer-Verlag

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Daverman, R.J. (1975). On the absence of tame disks in certain wild cells. In: Glaser, L.C., Rushing, T.B. (eds) Geometric Topology. Lecture Notes in Mathematics, vol 438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066112

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  • DOI: https://doi.org/10.1007/BFb0066112

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07137-2

  • Online ISBN: 978-3-540-37412-1

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