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Gul’ko, descriptive, and Gruenhage compact spaces

Espacios compactos de Gul’ko, desriptivos y de Gruenhage

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

We collect facts about Gul’ko, descriptive, Gruenhage, and fragmentable compact spaces. In several instances we provide direct proofs of the results discussed. We show how they reflect the geometrical structure of corresponding Banach spaces C(K). In particular, we provide proofs, by a simple transfer of Day’s norm, of recent renorming results for the duals C(K)* due to M. Raja and to R. Smith.

Resumen

Se recogen resultados acerca de espacios compactos de Gul’ko, descriptivos de Gruenhage y fragmentables. En ciertos casos se proporcionan pruebas directas de los resultados tratados. Se muestra cómo reflejan la estructura geométrica de los correspondientes espacios C(K). En particular, se proporcionan pruebas, mediante una simple transferencia de la norma de Day, de recientes resultados de renormamiento para los espacios duales C(K)* debidos a M. Raja y R. Smith.

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Authors and Affiliations

  1. Mathematical Institute, Czech Academy of Sciences, ŽZitná 25, 115 67, Prague 1, Czech Republic

    M. Fabian & V. Zizler

  2. Departamento de Matemática Aplicada and Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, C/Vera, s/n, 46022, Valencia, Spain

    V. Montesinos

Authors
  1. M. Fabian
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  2. V. Montesinos
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  3. V. Zizler
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Correspondence to M. Fabian.

Additional information

Dedicated to Professor Manuel Valdivia on the occasion of his 80th birthday, with our respect and admiration

Submitted by Manuel López-Pellicer

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Fabian, M., Montesinos, V. & Zizler, V. Gul’ko, descriptive, and Gruenhage compact spaces. RACSAM 104, 201–220 (2010). https://doi.org/10.5052/RACSAM.2010.14

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  • DOI: https://doi.org/10.5052/RACSAM.2010.14

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