A note on operators extending partial ultrametrics

Edward D. Tymchatyn; Michael M. Zarichnyi

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 515-524
  • ISSN: 0010-2628

Abstract

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We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.

How to cite

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Tymchatyn, Edward D., and Zarichnyi, Michael M.. "A note on operators extending partial ultrametrics." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 515-524. <http://eudml.org/doc/249559>.

@article{Tymchatyn2005,
abstract = {We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.},
author = {Tymchatyn, Edward D., Zarichnyi, Michael M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {partial ultrametric; extension operator; Assouad dimension; extension operator; Assouad dimension},
language = {eng},
number = {3},
pages = {515-524},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on operators extending partial ultrametrics},
url = {http://eudml.org/doc/249559},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Tymchatyn, Edward D.
AU - Zarichnyi, Michael M.
TI - A note on operators extending partial ultrametrics
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 515
EP - 524
AB - We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.
LA - eng
KW - partial ultrametric; extension operator; Assouad dimension; extension operator; Assouad dimension
UR - http://eudml.org/doc/249559
ER -

References

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