A metrizable completely regular ordered space
Hans-Peter A. Künzi; Stephen W. Watson
Commentationes Mathematicae Universitatis Carolinae (1994)
- Volume: 35, Issue: 4, page 773-778
- ISSN: 0010-2628
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topKünzi, Hans-Peter A., and Watson, Stephen W.. "A metrizable completely regular ordered space." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 773-778. <http://eudml.org/doc/247579>.
@article{Künzi1994,
abstract = {We construct a completely regular ordered space $(X,\{\mathcal \{T\}\},\le )$ such that $X$ is an $I$-space, the topology $\mathcal \{T\}$ of $X$ is metrizable and the bitopological space $(X,\{\mathcal \{T\}\}^\sharp ,\{\mathcal \{T\}\}^\{\flat \})$ is pairwise regular, but not pairwise completely regular. (Here $\{\mathcal \{T\}\}^\sharp $ denotes the upper topology and $\{\mathcal \{T\}\}^\flat $ the lower topology of $X$.)},
author = {Künzi, Hans-Peter A., Watson, Stephen W.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {completely regular ordered; strictly completely regular ordered; pairwise completely regular; pairwise regular; $I$-space},
language = {eng},
number = {4},
pages = {773-778},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A metrizable completely regular ordered space},
url = {http://eudml.org/doc/247579},
volume = {35},
year = {1994},
}
TY - JOUR
AU - Künzi, Hans-Peter A.
AU - Watson, Stephen W.
TI - A metrizable completely regular ordered space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 773
EP - 778
AB - We construct a completely regular ordered space $(X,{\mathcal {T}},\le )$ such that $X$ is an $I$-space, the topology $\mathcal {T}$ of $X$ is metrizable and the bitopological space $(X,{\mathcal {T}}^\sharp ,{\mathcal {T}}^{\flat })$ is pairwise regular, but not pairwise completely regular. (Here ${\mathcal {T}}^\sharp $ denotes the upper topology and ${\mathcal {T}}^\flat $ the lower topology of $X$.)
LA - eng
KW - completely regular ordered; strictly completely regular ordered; pairwise completely regular; pairwise regular; $I$-space
UR - http://eudml.org/doc/247579
ER -
References
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