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)

 
 

 

A category theorem for Tsuji functions


Author: Peter Colwell
Journal: Proc. Amer. Math. Soc. 51 (1975), 344-346
MSC: Primary 30A72
DOI: https://doi.org/10.1090/S0002-9939-1975-0374434-3
MathSciNet review: 0374434
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ H$ denotes the functions analytic in the open unit disk with the topology of uniform convergence on compact subsets, both the Tsuji functions in $ H$ and the functions in $ H$ with nonempty Tsuji sets comprise sets of first category in $ H$. A question is posed about the category of a class of functions containing the Tsuji functions.


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

  • [1] F. Bagemihl, Tsuji points and Tsuji functions, Comment Math. Univ. St. Paul. 17 (1968), 17-20. MR 38 #6072. MR 0237791 (38:6072)
  • [2] E. F. Collingwood and G. Piranian, Tsuji functions with segments of Julia, Math. Z. 84 (1964), 246-253. MR 29 #3637. MR 0166360 (29:3637)
  • [3] W. K. Hayman, The boundary behavior of Tsuji functions, Michigan Math. J. 15 (1968), 1-25. MR 37 #4265. MR 0228686 (37:4265)
  • [4] M. Tsuji, A theorem on the boundary behavior of a meromorphic function in $ \vert z\vert < 1$, Comment Math. Univ. St. Paul. 8 (1960), 53-55. MR 22 #11131. MR 0120377 (22:11131)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A72

Retrieve articles in all journals with MSC: 30A72


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0374434-3
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society