Coronas of ultrametric spaces

Igor V. Protasov

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 2, page 303-307
  • ISSN: 0010-2628

Abstract

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We show that, under CH, the corona of a countable ultrametric space is homeomorphic to ω * . 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.

How to cite

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Protasov, Igor V.. "Coronas of ultrametric spaces." Commentationes Mathematicae Universitatis Carolinae 52.2 (2011): 303-307. <http://eudml.org/doc/246421>.

@article{Protasov2011,
abstract = {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.},
author = {Protasov, Igor V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Stone-Čech compactification; ultrametric space; corona; Higson's corona; space of ends; Čech-Stone compactification; corona; ultrametric space},
language = {eng},
number = {2},
pages = {303-307},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Coronas of ultrametric spaces},
url = {http://eudml.org/doc/246421},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Protasov, Igor V.
TI - Coronas of ultrametric spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 2
SP - 303
EP - 307
AB - 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.
LA - eng
KW - Stone-Čech compactification; ultrametric space; corona; Higson's corona; space of ends; Čech-Stone compactification; corona; ultrametric space
UR - http://eudml.org/doc/246421
ER -

References

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  2. Engelking R., General Topology, PWN, Warzsawa, 1985. Zbl0684.54001
  3. Houghton C.H., 10.1112/jlms/s2-6.1.81, J. London Math. Soc. 6 (1972), 81–92. MR0316595DOI10.1112/jlms/s2-6.1.81
  4. van Mill J., Introduction to β ω , in Handbook of Set-Theoretical Topology, Chapter 11, Elsevier Science Publishers B.V., Amsterdam, 1984. Zbl0555.54004
  5. Protasov I.V., Normal ball structures, Math. Stud. 20 (2003), 3–16. Zbl1053.54503MR2019592
  6. Protasov I.V., 10.1016/j.topol.2004.09.005, Topology Appl. 149 (2005), 149–160. Zbl1068.54036MR2130861DOI10.1016/j.topol.2004.09.005
  7. Protasov I., Zarichnyi M., General asymptology, Math. Stud. Monogr. Ser. 12, VNTL, Lviv, 2007. Zbl1172.54002MR2406623

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