Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Embedding the hyperspaces of circle-like plane continua


Author: James T. Rogers
Journal: Proc. Amer. Math. Soc. 29 (1971), 165-168
MSC: Primary 54.55
DOI: https://doi.org/10.1090/S0002-9939-1971-0273578-0
MathSciNet review: 0273578
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The author shows that the hyperspace of continua of a circle-like plane continuum is embeddable in $ {E^3}$. The restriction to plane continua is necessary, for the hyperspace of a solenoid is homeomorphic to the cone over that solenoid and hence not embeddable in $ {E^3}$.


References [Enhancements On Off] (What's this?)

  • [1] Ralph Bennett and W. R. R. Transue, On embedding cones over circularly chainable continua, Proc. Amer. Math. Soc. 21 (1969), 275-276. MR 38 #6547. MR 0238271 (38:6547)
  • [2] R. H. Bing and R. J. Bean (Editors), Topology seminar, Wisconsin, 1965, Ann. of Math. Studies, no. 60, Princeton Univ. Press, Princeton, N. J., 1966. MR 34 #1974. MR 0202100 (34:1974)
  • [3] R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 456-483. MR 19, 300. MR 0087090 (19:300f)
  • [4] George W. Henderson, On the hyperspace of subcontinuum of an arc-like continuum, Notices Amer. Math. Soc. 17 (1970), 268. Abstract #672-644.
  • [5] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. MR 3, 315. MR 0006505 (3:315b)
  • [6] M. C. McCord, Embedding P-like compacta in manifolds, Canad. J. Math. 19 (1967), 321-332. MR 35 #3669. MR 0212804 (35:3669)
  • [7] J. Milnor, Differential topology, Princeton University, Princeton, N. J., 1958, (mimeographed).
  • [8] -, Topology from the differential viewpoint, The University Press of Virginia, Charlottesville, Va., 1965. MR 37 #2239. MR 0226651 (37:2239)
  • [9] T. Radó, On continuous mappings of Peano spaces, Trans. Amer. Math. Soc. 58 (1945), 420-454. MR 7, 282. MR 0014419 (7:282e)
  • [10] J. Segal, Hyperspaces of the inverse limit space, Proc. Amer. Math. Soc. 10 (1959), 706-709. MR 21 #7492. MR 0108780 (21:7492)
  • [11] W. R. R. Transue, On the hyperspace of subcontinua of the pseudoarc, Proc. Amer. Math. Soc. 18 (1967), 1074-1075. MR 36 #5901. MR 0222851 (36:5901)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.55

Retrieve articles in all journals with MSC: 54.55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0273578-0
Keywords: Circle-like, continuum, inverse limit, solenoid, disk-like continuum, hyperspace of continua
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society