| Title:
|
A note on the three-segment problem (English) |
| Author:
|
Doležal, Martin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
211-215 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
three-segment problem |
| Keyword:
|
cluster sets |
| MSC:
|
26B99 |
| MSC:
|
30D40 |
| idZBL:
|
Zbl 1212.30126 |
| idMR:
|
MR2535148 |
| DOI:
|
10.21136/MB.2009.140655 |
| . |
| Date available:
|
2010-07-20T17:58:38Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140655 |
| . |
| Reference:
|
[1] Bagemihl, F., Piranian, G., Young, G. S.: Intersections of cluster sets.Bul. Inst. Politeh. Iaşi, N. Ser. 5 (1959), 29-34. Zbl 0144.33203, MR 0117337 |
| Reference:
|
[2] Belna, C. L.: On the 3-segment property for complex-valued functions.Czech. Math. J. 22 (1972), 238-241. Zbl 0245.30030, MR 0301200 |
| Reference:
|
[3] Federer, H.: Geometric Measure Theory.Springer, Berlin (1996). Zbl 0874.49001 |
| Reference:
|
[4] Freiling, C., Humke, P. D., Laczkovich, M.: One old problem, one new, and their equivalence.Tatra Mt. Math. Publ. 24 (2002), 169-174. Zbl 1038.26003, MR 1939296 |
| Reference:
|
[5] Natanson, I. P.: Theory of Functions of a Real Variable.Ungar, New York (1955). MR 0067952 |
| . |
