Selections and weak orderability

Volume 203 / 2009

Michael Hrušák, Iván Martínez-Ruiz Fundamenta Mathematicae 203 (2009), 1-20 MSC: Primary 54C65; Secondary 54B20, 05C80. DOI: 10.4064/fm203-1-1

Abstract

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.

Authors

  • Michael HrušákInstituto de Matemáticas
    UNAM
    Apartado Postal 61-3
    Xangari, 58089
    Morelia, Michoacán, México
    e-mail
  • Iván Martínez-RuizInstituto de Matemáticas
    UNAM
    Apartado Postal 61-3
    Xangari, 58089
    Morelia, Michoacán, México
    e-mail

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