Skip to main content

Embeddings in shape theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 870)

Keywords

  • Piecewise Linear
  • Neighborhood Versus
  • Shape Theory
  • Regular Neighborhood
  • Shape Category

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. G. Bothe, Ein eindimensionales Kompaktum im E 3, das sich nicht Lagetreu in die Mengersche Universalkurve einbetten lässt, Fund. Math. 54(1964), pp. 251–258.

    MathSciNet  MATH  Google Scholar 

  2. J. Bryant, On embeddings of compacta in Euclidean space. Proc. Amer. Math. Soc. 23(1969), pp. 46–51.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J. Bryant, Approximating embeddings of polyhedra in codimension three, Trans. Amer. Math. Soc. 170 (1972), pp. 85–95.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. J. Bryant and C. L. Seebeck III, Locally nice embeddings in codimension three, Quart. J. Math. Oxford (2) 21 (1970), pp. 265–272.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. T. A. Chapman, Shapes of finite dimensional compacta, Fund. Math. 76 (1972), pp. 261–276.

    MathSciNet  MATH  Google Scholar 

  6. R. D. Edwards, The equivalence of close piecewise linear embeddings, Gen. Topology and its Appl. 5 (1975), pp. 147–180.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. R. D. Edwards, Demension theory, I in Geometric Topology, Lecture Notes in Mathematics, vol. 438, Springer-Verlag, New York (1975), pp. 195–211.

    CrossRef  Google Scholar 

  8. S. C. Ferry, A stable converse to the Vietoris-Smale theorem with applications to shape theory, Trans. Amer. Math. Soc. 261 (1980), pp. 369–386.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. V.K.A.M. Gugenheim, Piecewise linear isotopy and embeddings of elements and spheres (I), Proc. London Math. Soc. 3(3)(1953), pp. 29–53.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. L. Husch and I. Ivanšić, Embeddings and concordances of embeddings up to shape, preprint.

    Google Scholar 

  11. I. Ivanšić and R. B. Sher, A complement theorem for continua in a manifold, to appear in Topology Proceedings.

    Google Scholar 

  12. I. Ivanšić, R. B. Sher, and G. A. Venema, Complement theorems beyond the trivial range, to appear in Illinois J. Math.

    Google Scholar 

  13. D. R. McMillan, Jr. and H. Row, Tangled embeddings of 1-dimensional continua, Proc. Amer. Math. Soc. 22 (1969), pp. 378–385.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. J. Nagata, Modern Dimension Theory, John Wiley and Sons, New York, 1965.

    MATH  Google Scholar 

  15. S. Nowak, Some properties of fundamental dimension, Fund. Math. 85 (1974), pp. 211–117.

    MathSciNet  MATH  Google Scholar 

  16. T. B. Rushing, Topological Embeddings, Academic Press, New York, 1973.

    MATH  Google Scholar 

  17. J. R. Stallings, The piecewise-linear structure of Eucliden space, Proc. Cambridge Philos. Soc. 58 (1962), pp. 481–488.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. J. R. Stallings, The embedding of homotopy types into manifolds, Mimeographed Notes, Princeton University, 1965.

    Google Scholar 

  19. M. A. Štańko, The embedding of compacta in Euclidean space, Math USSR Sbornik 12 (1970), pp. 234–254.

    CrossRef  Google Scholar 

  20. M. A. Štańko, Approximation of compacta in E n in codimensions greater than two, Math. USSR Sbornik 19 (1973), pp. 625–636.

    Google Scholar 

  21. G. A. Venema, Embeddings of compacta with shape dimension in the trivial range, Proc. Amer. Math. Soc. 55 (1976), pp. 443–448.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. G. A. Venema, Neighborhoods of compacta in Euclidean space, Fund. Math. CIX (1980) pp. 71–78.

    MathSciNet  MATH  Google Scholar 

  23. G. A. Venema, An approximation theorem in shape theory, preprint.

    Google Scholar 

  24. E. C. Zeeman, Seminar on combinatorial topology, Mimeographed Notes, Institut des Hautes Etudes Scientifiques, Paris, 1963.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Venema, G.A. (1981). Embeddings in shape theory. In: Mardešić, S., Segal, J. (eds) Shape Theory and Geometric Topology. Lecture Notes in Mathematics, vol 870. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089715

Download citation

  • DOI: https://doi.org/10.1007/BFb0089715

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10846-7

  • Online ISBN: 978-3-540-38749-7

  • eBook Packages: Springer Book Archive