| Title:
|
Coronas of ultrametric spaces (English) |
| Author:
|
Protasov, I. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
303-307 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that, under CH, the corona of a countable ultrametric space is homeomorphic to $\omega^*$. As a corollary, we get the same statements for the Higson's corona of a proper ultrametric space and the space of ends of a countable locally finite group. (English) |
| Keyword:
|
Stone-Čech compactification |
| Keyword:
|
ultrametric space |
| Keyword:
|
corona |
| Keyword:
|
Higson's corona |
| Keyword:
|
space of ends |
| MSC:
|
54D35 |
| MSC:
|
54D80 |
| MSC:
|
54G05 |
| idZBL:
|
Zbl 1240.54087 |
| idMR:
|
MR2849052 |
| . |
| Date available:
|
2011-05-17T08:43:44Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141502 |
| . |
| Reference:
|
[1] Dranishnikov A.: Asymptotic topology.Russian Math. Surveys 55 (2000), 1085–1129. Zbl 1028.54032, MR 1840358, 10.1070/RM2000v055n06ABEH000334 |
| Reference:
|
[2] Engelking R.: General Topology.PWN, Warzsawa, 1985. Zbl 0684.54001 |
| Reference:
|
[3] Houghton C.H.: Ends of groups and associated first cohomology groups.J. London Math. Soc. 6 (1972), 81–92. MR 0316595, 10.1112/jlms/s2-6.1.81 |
| Reference:
|
[4] van Mill J.: Introduction to $\beta \omega $.in Handbook of Set-Theoretical Topology, Chapter 11, Elsevier Science Publishers B.V., Amsterdam, 1984. Zbl 0555.54004 |
| Reference:
|
[5] Protasov I.V.: Normal ball structures.Math. Stud. 20 (2003), 3–16. Zbl 1053.54503, MR 2019592 |
| Reference:
|
[6] Protasov I.V.: Coronas of balleans.Topology Appl. 149 (2005), 149–160. Zbl 1068.54036, MR 2130861, 10.1016/j.topol.2004.09.005 |
| Reference:
|
[7] Protasov I., Zarichnyi M.: General asymptology.Math. Stud. Monogr. Ser. 12, VNTL, Lviv, 2007. Zbl 1172.54002, MR 2406623 |
| . |
