A category theorem for Tsuji functions
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- by Peter Colwell PDF
- Proc. Amer. Math. Soc. 51 (1975), 344-346 Request permission
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
- F. Bagemihl, Tsuji points and Tsuji functions, Comment. Math. Univ. St. Paul. 17 (1968), 17–20. MR 237791
- E. F. Collingwood and George Piranian, Tsuji functions with segments of Julia, Math. Z. 84 (1964), 246–253. MR 166360, DOI 10.1007/BF01112579
- W. K. Hayman, The boundary behaviour of Tsuji functions, Michigan Math. J. 15 (1968), 1–25. MR 228686
- Masatsugu Tsuji, A theorem on the boundary behaviour of a meromorphic function in $|z|<1$, Comment. Math. Univ. St. Paul. 8 (1960), 53–55. MR 120377
Additional Information
- © Copyright 1975 American Mathematical Society
- 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