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)

 
 

 

Upper semicontinuous collections of continua in class $ W$


Author: C. Wayne Proctor
Journal: Proc. Amer. Math. Soc. 88 (1983), 338-340
MSC: Primary 54F20; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1983-0695271-0
MathSciNet review: 695271
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A continuum is proven to be in Class $ W$ if it can be decomposed into an upper semicontinuous collection of $ C$-sets, each of which is contained in Class $ W$, and if the upper semicontinuous decomposition space thus formed is in Class $ W$.


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

  • [1] H. Cook, Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241-249. MR 0220249 (36:3315)
  • [2] G. A. Feuerbacher, Weakly chainable circle-like continua, Dissertation, Univ. of Houston, Houston, 1974.
  • [3] J. Grispolakis and E. D. Tymchatyn, Continua which admit only certain classes of onto mappings, Topology Proc. 3 (1978), 347-382. MR 540501 (80k:54063)
  • [4] -, Continua which are images of weakly confluent mappings only, Houston J. Math. 5 (1979), 483-502. MR 567908 (81d:54008)
  • [5] -, On confluent mappings and essential mappings--a survey, Rocky Mountain J. Math. 11 (1981), 131-153. MR 612135 (82k:54055)
  • [6] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. MR 0125557 (23:A2857)
  • [7] W. T. Ingram, Atriodic tree-like continua and the span of mappings, Topology Proc. 1 (1976), 329-333.
  • [8] -, $ C$-sets and mappings of continua, Topology Conf. (to appear).
  • [9] A. Lelek, Report on weakly confluent mappings, (Topology Conf., Virginia Polytechnic Inst. and State Univ., 1973), Lecture Notes in Math., vol. 375, Springer, Berlin, 1974, pp. 168-170. MR 0358668 (50:11127)
  • [10] R. L. Moore, Foundatins of point set theory, Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R.I., 1962. MR 0150722 (27:709)
  • [11] D. R. Read, Confluent and related mapping, Colloq. Math. 29 (1974), 233-239. MR 0367903 (51:4145)
  • [12] A. D. Wallace, The position of $ C$-sets in semigroups, Proc. Amer. Math. Soc. 6 (1955), 639-642. MR 0071709 (17:172d)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F20, 54C10

Retrieve articles in all journals with MSC: 54F20, 54C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0695271-0
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society