Coronas of ultrametric spaces

Igor V. Protasov

Commentationes Mathematicae Universitatis Carolinae (2011)

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

Abstract

top
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

top

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

top
  1. Dranishnikov A., 10.1070/RM2000v055n06ABEH000334, Russian Math. Surveys 55 (2000), 1085–1129. Zbl1028.54032MR1840358DOI10.1070/RM2000v055n06ABEH000334
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.