Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T07:08:10.882Z Has data issue: false hasContentIssue false
  • English
  • Français

Embedding Circle-Like Continua in E3

Published online by Cambridge University Press:  20 November 2018

B. J. Ball  and
R. B. Sher
B. J. Ball
Affiliation:
University of Georgia, Athens, Georgia
R. B. Sher
Affiliation:
University of Georgia, Athens, Georgia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A space X is locally planar if each point of X has a neighborhood which is embeddable in the plane. If X is a closed, locally planar subset of E3, we will say that X is locally tame if each point of X has a neighborhood in X which lies on a tame disk in E3; if every cell-like subset of X has such a neighborhood, we say that X is strongly locally tame.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 791 - 805
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Ball, B. J. and Sher, R. B., Extending cell-like maps on manifolds (to appear in Trans. Amer. Math. Soc).Google Scholar
2. Bennet, Ralph and Transue, W. R. R., On embedding cones over circularly chainable continua, Proc. Amer. Math. Soc. 21 (1969), 275–276.Google Scholar
3. Bing, R. H., Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43–51.Google Scholar
4. Bing, R. H., A simple closed curve that pierces no disk, J. Math. Pures Appl. 35 (1956), 337–343.Google Scholar
5. Bing, R. H., Upper semicontinuous decompositions of E3, Ann. of Math. 65 (1957), 363–374.Google Scholar
6. Bing, R. H., Embedding circle-like continua in the plane, Can. J. Math. 14 (1962), 113–128.Google Scholar
7. Borsuk, Karol, Concerning homotopy properties of compacta. Fund. Math. 62 (1968), 223–254.Google Scholar
8. Borsuk, Karol, Concerning the notion of the shape of compacta, Proc. Inter. Symposium on Topology and its Applications, pp. 98–104, Beograd, 1969.Google Scholar
9. Karol, Borsuk, On movable compacta, Fund. Math. 66 (1969), 137–146.Google Scholar
10. Burgess, C. E. and Cannon, J. W., Embeddings of surfaces in E3, Rocky Mountain J. Math. 1 (1971) 259–344.Google Scholar
11. Fearnley, Lawrence, The pseudo-circle is unique, Trans. Amer. Math. Soc. 149 (1970), 45–63.Google Scholar
12. Fox, Ralph H. and Artin, Emil, Some wild cells and spheres in three-dimensional space, Ann. of Math. 49 (1948), 979–990.Google Scholar
13. George, Henderson W., On the hyper space of subcontinua of an arc-like continuum, Proc. Amer. Math. Soc. 27 (1971), 416–417.Google Scholar
14. Ingram, W. T., Concerning nonplanar circle-like continua, Can. J. Math. 19 (1967), 242–250.Google Scholar
15. Isbell, J. R., Embeddings of inverse limits, Ann. of Math. 70 (1959), 73–84.Google Scholar
16. Kelley, J. L., Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22–36.Google Scholar
17. Lacher, R. C., Cell-like mappings, I, Pacific J. Math. 30 (1969), 717–731.Google Scholar
18. Marešić, Sibe and Jack, Segal, Shapes of compacta and ANR systems, Fund. Math. 72 (1971), 41–59.Google Scholar
19. Rogers, James T., Jr., Embedding the hyperspaces of circle-like plane continua, Proc. Amer. Math. Soc. 29 (1971), 165–168.Google Scholar
20. Segal, Jack, Hyperspaces of the inverse limit space, Proc. Amer. Math. Soc. 10 (1959), 706–709.Google Scholar
21. Sher, R. B., Realizing cell-like maps in Euclidean space, General Topology and Appl. 2 (1972), 75–89.Google Scholar
22. Transue, W. R. R., On the hyperspace of subcontinua of the pseudoarc, Proc. Amer. Math. Soc. 18 (1967), 1074–1075.Google Scholar
23. Whitney, H., Regular families of curves, Ann. of Math. 34 (1933), 244–270.Google Scholar