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Semicellular sets in crumpled cubes

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Geometric Topology

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

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References

  1. R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 456–483.

    Article  MathSciNet  MATH  Google Scholar 

  2. _____, A surface is tame if its complement is 1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. _____, Approximating surfaces from the side, Ann. of Math. (2) 77 (1963), 145–192.

    Article  MathSciNet  MATH  Google Scholar 

  5. _____, Improving the side approximation theorem, Trans. Amer. Math. Soc. 116 (1965), 511–525.

    Article  MathSciNet  MATH  Google Scholar 

  6. Morton Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960), 74–76.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. E. Burgess, Characterizations of tame surfaces in E 3, Trans. Amer. Math. Soc. 114 (1965), 80–97.

    MathSciNet  MATH  Google Scholar 

  8. _____, Criteria for a 2-sphere to be tame modulo two points, Michigan Math. J. 14 (1967), 321–330.

    Article  MathSciNet  MATH  Google Scholar 

  9. C. E. Burgess and J. W. Cannon, Embeddings of surfaces in E 3, Rocky Mountain J. Math. 1 (1971), 259–344.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. W. Cannon, Characterization of taming sets on 2-spheres, Trans. Amer. Math. Soc. 147 (1970), 289–299.

    MathSciNet  MATH  Google Scholar 

  11. _____, New proofs of Bing’s approximation theorems for surfaces, Pacific J. Math. 46 (1973), 361–379.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. J. Daverman, A new proof for the Hosay-Lininger theorem about crumpled cubes, Proc. Amer. Math. Soc. 23 (1969), 52–54.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. J. Daverman and W. T. Eaton, Universal crumpled cubes, Topology 11 (1972), 223–235.

    Article  MathSciNet  MATH  Google Scholar 

  14. __________, The existence of nontrivial universal crumpled cubes, Notices Amer. Math. Soc. 10 (1969), 234–235.

    Google Scholar 

  15. P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres in E 3, Proc. Amer. Math. Soc. 11 (1960), 832–836.

    MathSciNet  MATH  Google Scholar 

  16. R. H. Fox and E. Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979–990.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. S. Gillman, Note concerning a wild sphere of Bing, Duke Math. J. 31 (1964), 247–254.

    Article  MathSciNet  MATH  Google Scholar 

  18. Norman Hosay, The sum of a real cube and a crumpled cube is S 3, Notices Amer. Math. Soc. 10 (1963), 666. See also Errata 11 (1964), 152.

    Google Scholar 

  19. L. L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534–549.

    Article  MathSciNet  MATH  Google Scholar 

  20. F. M. Lister, Simplifying intersections of disks in Bing’s side approximation theorem, Pacific J. Math. 22 (1967), 281–295.

    Article  MathSciNet  MATH  Google Scholar 

  21. L. D. Loveland, Tame subsets of spheres in E 3, Pacific J. Math. 19 (1966), 489–517.

    Article  MathSciNet  MATH  Google Scholar 

  22. _____, Piercing points of crumpled cubes, Trans. Amer. Math. Soc. 143 (1969), 145–152.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. M. Martin, The sum of two crumpled cubes, Michigan Math. J. 13 (1966), 147–151.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. R. McMillan, A criterion for cellularity in a manifold, Ann. of Math. (2) 79 (1964), 327–337.

    Article  MathSciNet  MATH  Google Scholar 

  25. _____, Some topological properties of piercing points, Pacific J. Math. 22 (1967), 313–322.

    Article  MathSciNet  MATH  Google Scholar 

  26. _____, Piercing a disk along a cellular set, Proc. Amer. Math. Soc. 19 (1968), 153–157.

    Article  MathSciNet  MATH  Google Scholar 

  27. D. G. Stewart, Cellular subsets of the 3-sphere, Trans. Amer. Math. Soc. 114 (1965), 10–22.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. University of Utah, Salt Lake City, Utah

    C. E. Burgess

Authors
  1. C. E. Burgess
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Leslie Curtis Glaser Thomas Benjamin Rushing

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© 1975 Springer-Verlag

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Burgess, C.E. (1975). Semicellular sets in crumpled cubes. In: Glaser, L.C., Rushing, T.B. (eds) Geometric Topology. Lecture Notes in Mathematics, vol 438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066106

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  • DOI: https://doi.org/10.1007/BFb0066106

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07137-2

  • Online ISBN: 978-3-540-37412-1

  • eBook Packages: Springer Book Archive

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