| Title:
|
Classification of spaces of continuous functions on ordinals (English) |
| Author:
|
Genze, Leonid V. |
| Author:
|
Gul'ko, Sergei P. |
| Author:
|
Khmyleva, Tat'ana E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
365-370 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We conclude the classification of spaces of continuous functions on ordinals carried out by Górak [Górak R., {Function spaces on ordinals}, Comment. Math. Univ. Carolin. {46} (2005), no. 1, 93--103]. This gives a complete topological classification of the spaces $C_p([0,\alpha])$ of all continuous real-valued functions on compact segments of ordinals endowed with the topology of pointwise convergence. Moreover, this topological classification of the spaces $C_p([0,\alpha])$ completely coincides with their uniform classification. (English) |
| Keyword:
|
space of continuous functions |
| Keyword:
|
pointwise topology |
| Keyword:
|
homeomorphism of function spaces |
| Keyword:
|
uniform homeomorphism |
| Keyword:
|
ordinal number |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 06940876 |
| idMR:
|
MR3861558 |
| DOI:
|
10.14712/1213-7243.2015.250 |
| . |
| Date available:
|
2018-09-10T12:15:51Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147403 |
| . |
| Reference:
|
[1] Arhangel'skij A. V.: On linear homeomorphisms of function spaces.Sov. Math., Dokl. 25 (1982), 852–855; translation from Dokl. Akad. Nauk SSSR 264 (1982), 1289–1292 (Russian). MR 0664477 |
| Reference:
|
[2] Baars J. A., de Groot J. A. M.: On Topological and Linear Equivalence of Certain Function Spaces.CWI Tract 86, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1992. Zbl 0755.54007, MR 1182148 |
| Reference:
|
[3] Bessaga C., Pełczyński A.: Spaces of continuous functions. IV. On isomorphic classification of spaces $C(S)$.Studia Math. 19 (1960), 53–62. MR 0113132, 10.4064/sm-19-1-53-62 |
| Reference:
|
[4] Engelking R.: General Topology.Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[5] Górak R.: Function spaces on ordinals.Comment. Math. Univ. Carolin. 46 (2005), no. 1, 93–103. MR 2175862 |
| Reference:
|
[6] Gul'ko S. P.: Free topological groups and a space of continuous functions on ordinals.Vestnik of Tomsk State University (2003), no. 280, 34–38 (Russian). |
| Reference:
|
[7] Gul'ko S. P., Os'kin A. V.: Isomorphic classification of spaces of continuous functions on totally ordered compact sets.Funkcional Anal. i Priložen. 9 (1975) no. 1, 56–57 (Russian). MR 0427401 |
| Reference:
|
[8] Kislyakov S. V.: Classification of spaces of continuous functions of ordinals.Siberian Math. J. 16 (1975), no. 2, 226–231; translated from Sibirskii Matematicheskij Zhurnal 16 (1975), no. 2, 293–300 (Russian). MR 0377490, 10.1007/BF00967506 |
| Reference:
|
[9] Semadeni Z.: Banach spaces non-isomorphic to their Cartesian squares. II.Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 8 (1960), 81–84. MR 0115074 |
| Reference:
|
[10] Tkachuk V. V.: A $C_p$-Theory Problem Book.Topological and Function Spaces, Problem Books in Mathematics, Springer, New York, 2011. MR 3024898 |
| . |
