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Metrizability and Coconnectedness

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Abstract

Solving the problem stated in Sichler and Trnková, Topol. Its Appl., 142: 159–179, 2004, we construct metrics μ, ν on a set P such that the spaces X=(P,μ) and Y=(P,ν) have the same monoid of all continuous selfmaps, the space Y is coconnected (in the sense that every continuous map Y×Y→Y depends on at most one coordinate) while X is not. Also, properties of the forgetful functors Metr → Unif → Top are investigated for the “simultaneous variant” of the above problem.

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Authors and Affiliations

  1. Mathematical Institute of Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Věra Trnková

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  1. Věra Trnková
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Correspondence to Věra Trnková.

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Supported by the Grant Agency of Czech Republic under grant 201/06/0664 and by the project of Ministry of Education of Czech Republic MSM 0021620839.

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Trnková, V. Metrizability and Coconnectedness. Appl Categor Struct 15, 621–631 (2007). https://doi.org/10.1007/s10485-006-9036-5

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  • DOI: https://doi.org/10.1007/s10485-006-9036-5

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