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Are Eberlein–Grothendieck scattered spaces \(\sigma \)-discrete?

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Abstract

A space \(X\) is Eberlein–Grothendieck if \(X\subset C_p(K)\) for some compact space \(K.\) In this paper we address the problem of whether such a space \(X\) is \(\sigma \)-discrete whenever it is scattered. We show that if \(w(K)\le \omega _1\) then such \(X\) is \(\sigma \)-discrete whenever it is locally compact or locally countable.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, 30100, Murcia, Spain

    Antonio Avilés & David Guerrero Sánchez

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  1. Antonio Avilés
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  2. David Guerrero Sánchez
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Correspondence to David Guerrero Sánchez.

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D. G. Sánchez is supported by FEDER, PROJECT MTM 2011-25377.

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Avilés, A., Sánchez, D.G. Are Eberlein–Grothendieck scattered spaces \(\sigma \)-discrete?. RACSAM 108, 849–859 (2014). https://doi.org/10.1007/s13398-013-0146-2

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  • DOI: https://doi.org/10.1007/s13398-013-0146-2

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