About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Protasov, I. V.
Coronas of ultrametric spaces. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 52 (2011), issue 2, pp. 303-307
MSC: 54D35, 54D80, 54G05 | MR 2849052 | Zbl 1240.54087
Keywords:
Stone-Čech compactification; ultrametric space; corona; Higson's corona; space of ends
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.
References:
[1] Dranishnikov A.: Asymptotic topology. Russian Math. Surveys 55 (2000), 1085–1129. DOI 10.1070/RM2000v055n06ABEH000334 | MR 1840358 | Zbl 1028.54032
[2] Engelking R.: General Topology. PWN, Warzsawa, 1985. Zbl 0684.54001
[3] Houghton C.H.: Ends of groups and associated first cohomology groups. J. London Math. Soc. 6 (1972), 81–92. DOI 10.1112/jlms/s2-6.1.81 | MR 0316595
[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
[5] Protasov I.V.: Normal ball structures. Math. Stud. 20 (2003), 3–16. MR 2019592 | Zbl 1053.54503
[6] Protasov I.V.: Coronas of balleans. Topology Appl. 149 (2005), 149–160. DOI 10.1016/j.topol.2004.09.005 | MR 2130861 | Zbl 1068.54036
[7] Protasov I., Zarichnyi M.: General asymptology. Math. Stud. Monogr. Ser. 12, VNTL, Lviv, 2007. MR 2406623 | Zbl 1172.54002
Partner of
EuDML logo