Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
three-segment problem; cluster sets
three-segment problem; cluster sets
Summary:
We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.
References:
[1] Bagemihl, F., Piranian, G., Young, G. S.: Intersections of cluster sets. Bul. Inst. Politeh. Iaşi, N. Ser. 5 (1959), 29-34. MR 0117337 | Zbl 0144.33203
[2] Belna, C. L.: On the 3-segment property for complex-valued functions. Czech. Math. J. 22 (1972), 238-241. MR 0301200 | Zbl 0245.30030
[3] Federer, H.: Geometric Measure Theory. Springer, Berlin (1996). Zbl 0874.49001
[4] Freiling, C., Humke, P. D., Laczkovich, M.: One old problem, one new, and their equivalence. Tatra Mt. Math. Publ. 24 (2002), 169-174. MR 1939296 | Zbl 1038.26003
[5] Natanson, I. P.: Theory of Functions of a Real Variable. Ungar, New York (1955). MR 0067952
Search
Partner of
