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Topological calculus for separating points from closed sets by maps

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Abstract

Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski’s topological calculus.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del País Vasco UPV/EHU, Apdo. 644, 480 80, Bilbao, Spain

    Javier Gutiérrez García

  2. Wydział Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, ul. Umultowska 87, 61-614, Poznań, Poland

    Tomasz Kubiak

Authors
  1. Javier Gutiérrez García
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  2. Tomasz Kubiak
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Corresponding author

Correspondence to Javier Gutiérrez García.

Additional information

The authors acknowledge financial support from the Ministry of Science and Innovation of Spain under grant MTM2009-12872-C02-02. The first named author also acknowledges financial support from the UPV-EHU under grant GIU07/27.

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García, J.G., Kubiak, T. Topological calculus for separating points from closed sets by maps. Czech Math J 62, 257–264 (2012). https://doi.org/10.1007/s10587-012-0010-0

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  • DOI: https://doi.org/10.1007/s10587-012-0010-0

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