On half-completion and bicompletion of quasi-metric spaces

Elena Alemany; Salvador Romaguera

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 4, page 749-756
  • ISSN: 0010-2628

Abstract

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We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space X is quasi-metric if and only if X is finite.

How to cite

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Alemany, Elena, and Romaguera, Salvador. "On half-completion and bicompletion of quasi-metric spaces." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 749-756. <http://eudml.org/doc/247902>.

@article{Alemany1996,
abstract = {We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space $X$ is quasi-metric if and only if $X$ is finite.},
author = {Alemany, Elena, Romaguera, Salvador},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasi-metric; quasi-uniform; half-completion; bicompletion; uniformly weakly regular; quasi-metric; quasi-uniform space; half-completion; bicompletion; uniformly weakly regular space},
language = {eng},
number = {4},
pages = {749-756},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On half-completion and bicompletion of quasi-metric spaces},
url = {http://eudml.org/doc/247902},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Alemany, Elena
AU - Romaguera, Salvador
TI - On half-completion and bicompletion of quasi-metric spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 4
SP - 749
EP - 756
AB - We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space $X$ is quasi-metric if and only if $X$ is finite.
LA - eng
KW - quasi-metric; quasi-uniform; half-completion; bicompletion; uniformly weakly regular; quasi-metric; quasi-uniform space; half-completion; bicompletion; uniformly weakly regular space
UR - http://eudml.org/doc/247902
ER -

References

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