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)

 
 

 

The preservation of atriodicity by semiconfluent mappings


Author: James F. Davis
Journal: Proc. Amer. Math. Soc. 100 (1987), 579-584
MSC: Primary 54F20; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1987-0891167-3
MathSciNet review: 891167
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Grace and Vought have proven that the image of a chainable continuum under a semiconfluent mapping is atriodic. This motivates the question of whether the semiconfluent image of an atriodic continuum is atriodic. In this paper this question is answered affirmatively.


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

  • [1] E. E. Grace and E. J. Vought, Semi-confluent and weakly confluent images of tree-like and atriodic continua, Fund. Math. 101 (1978), 151-158. MR 518350 (80c:54032)
  • [2] J. Grispolakis and E. D. Tymchatyn, Semi-confluent mappings and acyclicity, Houston J. Math. 4 (1978), 343-357. MR 514248 (80e:54051)
  • [3] -, On the Čech cohomology of continua with no $ n$-ods, Houston J. Math. 11 (1985), 505-513. MR 837989 (88c:54019)
  • [4] T. Maćkowiak, Semi-confluent mappings and their invariants, Fund. Math. 79 (1973), 251-264. MR 0321044 (47:9577)
  • [5] -, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.), No. 158, PWN, Warsaw, 1979. MR 522934 (81a:54034)
  • [6] R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloq. Publ, vol. 13, Amer. Math. Soc., Providence, R. I., 1962. MR 0150722 (27:709)
  • [7] R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439-460. MR 0010968 (6:96d)

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/S0002-9939-1987-0891167-3
Keywords: Semiconfluent mappings, atriodic continua
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society