Selections and weak orderability

Michael Hrušák¹ ; Iván Martínez-Ruiz¹

¹Instituto de Matemáticas UNAM Apartado Postal 61-3 Xangari, 58089 Morelia, Michoacán, México

Fundamenta Mathematicae, Tome 203 (2009) no. 1, pp. 1-20

Résumé

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.

Détail

DOI : 10.4064/fm203-1-1

Keywords: answer question van mill wattel showing there separable locally compact space which admits continuous weak selection weakly orderable furthermore separable space which admits continuous weak selection covered weakly orderable spaces finally partial answer question gutev nogura showing separable space which admits continuous weak selection admits continuous selection finite sets