A continuous operator extending ultrametrics

I. Stasyuk; Edward D. Tymchatyn

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 1, page 141-151
  • ISSN: 0010-2628

Abstract

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The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.

How to cite

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Stasyuk, I., and Tymchatyn, Edward D.. "A continuous operator extending ultrametrics." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 141-151. <http://eudml.org/doc/32488>.

@article{Stasyuk2009,
abstract = {The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.},
author = {Stasyuk, I., Tymchatyn, Edward D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ultrametric; space of partial ultrametrics; continuous extension operator; ultrametric; space of partial ultrametrics; continuous extension operator},
language = {eng},
number = {1},
pages = {141-151},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A continuous operator extending ultrametrics},
url = {http://eudml.org/doc/32488},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Stasyuk, I.
AU - Tymchatyn, Edward D.
TI - A continuous operator extending ultrametrics
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 141
EP - 151
AB - The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.
LA - eng
KW - ultrametric; space of partial ultrametrics; continuous extension operator; ultrametric; space of partial ultrametrics; continuous extension operator
UR - http://eudml.org/doc/32488
ER -

References

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  14. Stasyuk I., Operators of simultaneous extensions partial ultrametrics, Math. Methods and Phys.-Mech. Fields 49 (2006), 2 27--32 (Ukrainian). (2006) MR2259425
  15. Stasyuk I., Tymchatyn E.D., A note on uniformly continuous selections of multivalued maps, submitted to Topology Appl. 
  16. Tymchatyn E.D., Zarichnyi M., 10.1090/S0002-9939-04-07413-1, Proc. Amer. Math. Soc. 132 (2004), 2799--2807. (2004) Zbl1050.54011MR2054807DOI10.1090/S0002-9939-04-07413-1
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