We answer a question of van Mill and Wattel by showing that there is a separable locally compact space which admits a continuous weak selection but is not weakly orderable. Furthermore, we show that a separable space which admits a continuous weak selection can be covered by two weakly orderable spaces. Finally, we give a partial answer to a question of Gutev and Nogura by showing that a separable space which admits a continuous weak selection admits a continuous selection for all finite sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-1,
author = {Michael Hru\v s\'ak and Iv\'an Mart\'\i nez-Ruiz},
title = {Selections and weak orderability},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {1-20},
zbl = {1170.54008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-1}
}
Michael Hrušák; Iván Martínez-Ruiz. Selections and weak orderability. Fundamenta Mathematicae, Tome 205 (2009) pp. 1-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-1/