Article
| 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 |
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| Category: | math |
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| 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. |
| Keyword: | Stone-Čech compactification |
| Keyword: | ultrametric space |
| Keyword: | corona |
| Keyword: | Higson's corona |
| Keyword: | space of ends |
| MSC: | 54D35 |
| MSC: | 54D80 |
| MSC: | 54G05 |
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| Date available: | 2011-05-17T08:43:44Z |
| Last updated: | 2012-08-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/141502 |
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| Reference: | [1] Dranishnikov A.: Asymptotic topology.Russian Math. Surveys 55 (2000), 1085–1129. Zbl 1028.54032, MR 1840358 |
| 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 |
| 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 |
| Reference: | [7] Protasov I., Zarichnyi M.: General asymptology.Math. Stud. Monogr. Ser. 12, VNTL, Lviv, 2007. Zbl 1172.54002, MR 2406623 |
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