Selections and weak orderability
Tom 203 / 2009
Fundamenta Mathematicae 203 (2009), 1-20 MSC: Primary 54C65; Secondary 54B20, 05C80. DOI: 10.4064/fm203-1-1
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.