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)



Weakly confluent mappings and finitely-generated cohomology

Author: James T. Rogers
Journal: Proc. Amer. Math. Soc. 78 (1980), 436-438
MSC: Primary 54F20; Secondary 54B20
MathSciNet review: 553390
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if $ {H^1}(X)$ is finitely generated, then $ C(X)$, the hyperspace of subcontinua of X, has dimension 2.

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

  • [1] C. Eberhart and S. B. Nadler, Jr., The dimension of certain hyperspaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 1027-1034. MR 0303513 (46:2650)
  • [2] M. K. Fort, Jr., Images of plane continua, Amer. J. Math. 81 (1959), 541-546. MR 0106441 (21:5173)
  • [3] W. Hurewicz and J. Wallman, Dimension theory, Princeton Univ. Press, Princeton, N. J., 1948.
  • [4] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. MR 0006505 (3:315b)
  • [5] A. Lelek, A classification of mappings pertinent to curve theory, Proc. Univ. of Oklahoma Topology Conf., University of Oklahoma, Norman, 1972, pp. 97-103. MR 0358667 (50:11126)
  • [6] Wayne Lewis, Dimensons of hereditarily indecomposable continua, Proc. Geometric Topology Conf., Warsaw, 1978 (to appear).
  • [7] -, Monotone maps of hereditarily indecomposable continua, Proc. Amer. Math. Soc. 75 (1979), 361-364. MR 532166 (82g:54051)
  • [8] S. Mazurkiewicz, Sur l'existence des continus indécomposables, Fund. Math. 25 (1935), 327-328.
  • [9] E. D. Tymchatyn, Hyperspaces of hereditarily indecomposable plane continua, Proc. Amer. Math. Soc. 56 (1976), 300-302. MR 0405334 (53:9128)
  • [10] David Wilson, Open mappings of the universal curve onto continuous curves, Trans. Amer. Math. Soc. 168 (1972), 497-515. MR 0298630 (45:7682)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F20, 54B20

Retrieve articles in all journals with MSC: 54F20, 54B20

Additional Information

Keywords: Weakly confluent, monotone, dimension, hyperspace, hereditarily indecomposable continuum
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society