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Embedding coverings into bundles with applications

About this Title

P. F. Duvall and L. S. Husch

Publication: Memoirs of the American Mathematical Society
Publication Year: 1982; Volume 38, Number 263
ISBNs: 978-0-8218-2263-0 (print); 978-1-4704-0670-7 (online)
DOI: https://doi.org/10.1090/memo/0263
MathSciNet review: 660215
MSC: Primary 57R40; Secondary 57N25, 57N35, 57Q35

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Table of Contents

Chapters

  • Introduction
  • Part I. Embedding finite covers into bundles
  • 1. Removing singularities of maps
  • 2. Singularities of maps into bundles
  • 3. Embedding covering spaces into bundles
  • 4. The obstruction
  • Part II. Embedding manifold-like continua up to shape
  • 5. Applications of Part I to embedding continua up to shape
  • 6. An $n$-manifold-like compactum which does not embed up to shape in $\mathbb {R}^{2n}$
  • 7. Singularities of coverings of immersions
  • 8. Embedding up to shape manifold-like continua whose factors need not embed
  • 9. Embedding double coverings
  • 10. An example
  • 11. $n$-manifold-like continua which do not embed up to shape in $\mathbb {R}^{2n}$