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)

 
 

 

Some nowhere equicontinuous homeomorphisms


Author: Ki Woong Kim
Journal: Proc. Amer. Math. Soc. 60 (1976), 304-308
MSC: Primary 57E20; Secondary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1976-0423391-0
MathSciNet review: 0423391
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a nowhere equicontinuous homeomorphism can be defined on a compact polyhedron X if and only if X does not have cell decomposition which contains a principal 1-cell. It is also shown that for each locally connected contractible continuum C in the plane, there is a nowhere equicontinuous homeomorphism $ {h_c}$ on a disk in the plane such that the fixed point set of $ {h_c}$ is C.


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

  • [1] Robert Ellis, Lectures on topological dynamics, Benjamin, New York, 1969. MR 42 #2463. MR 0267561 (42:2463)
  • [2] P.-F. Lam, The intermediate transformation groups, Lecture Notes in Math., vol. 318, Springer-Verlag, Berlin and New York, 1973, pp. 174-180. MR 0391050 (52:11872)
  • [3] H. C. Griffith and L. R. Howell, Jr., Strongly cellular cells in $ {E^3}$ are tame, Fund. Math. 65 (1969), 23-32. MR 39 #6289. MR 0244976 (39:6289)
  • [4] C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Springer-Verlag, New York, 1972. MR 50 #3236. MR 0350744 (50:3236)
  • [5] Arlo W. Schurle, Strongly cellular subsets of $ {E^3}$, Fund. Math. 80 (1973), no. 3, 207-212. MR 48 #7293. MR 0328951 (48:7293)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57E20, 54H20

Retrieve articles in all journals with MSC: 57E20, 54H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0423391-0
Keywords: Equicontinuous homeomorphism, irregular set, dense orbit, principal ncell, strong cellularity
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society