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Weak selections and weak orderability of function spaces

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Abstract

It is proved that for a zero-dimensional space X, the function space C p (X, 2) has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if X is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space E, the function space C p (X, E) is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial positive answer to a question posed by van Mill and Wattel.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000, South Africa

    Valentin Gutev

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  1. Valentin Gutev
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Correspondence to Valentin Gutev.

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This work is based upon research supported by the NRF of South Africa.

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Gutev, V. Weak selections and weak orderability of function spaces. Czech Math J 60, 273–281 (2010). https://doi.org/10.1007/s10587-010-0015-5

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  • DOI: https://doi.org/10.1007/s10587-010-0015-5

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