Hyperspace selections avoiding points

Valentin Gutev

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 3, page 351-364
  • ISSN: 0010-2628

Abstract

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We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic order, and gives a characterisation of the so called weakly cyclically orderable spaces.

How to cite

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Gutev, Valentin. "Hyperspace selections avoiding points." Commentationes Mathematicae Universitatis Carolinae 62 63.3 (2022): 351-364. <http://eudml.org/doc/299031>.

@article{Gutev2022,
abstract = {We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic order, and gives a characterisation of the so called weakly cyclically orderable spaces.},
author = {Gutev, Valentin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Vietoris topology; continuous selection; weak selection; weakly orderable space; weakly cyclically orderable space},
language = {eng},
number = {3},
pages = {351-364},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hyperspace selections avoiding points},
url = {http://eudml.org/doc/299031},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Gutev, Valentin
TI - Hyperspace selections avoiding points
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 3
SP - 351
EP - 364
AB - We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic order, and gives a characterisation of the so called weakly cyclically orderable spaces.
LA - eng
KW - Vietoris topology; continuous selection; weak selection; weakly orderable space; weakly cyclically orderable space
UR - http://eudml.org/doc/299031
ER -

References

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