Skip to main content

On the absence of tame disks in certain wild cells

  • Conference paper
  • First Online:
Geometric Topology

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Leslie Curtis Glaser Thomas Benjamin Rushing

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07137-2

  • Online ISBN: 978-3-540-37412-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics