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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Mardešić Conjecture and free products of Boolean algebras
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by Gonzalo Martínez-Cervantes and Grzegorz Plebanek PDF
Proc. Amer. Math. Soc. 147 (2019), 1763-1772 Request permission

Abstract:

We show that for every $d\ge 1$, if $L_1,\ldots , L_d$ are linearly ordered compact spaces and there is a continuous surjection \[ L_1\times L_2\times \dots \times L_d\to K_1\times K_2\times \cdots \times K_{d}\times K_{d+1},\] where all the spaces $K_i$ are infinite, then $K_i, K_j$ are metrizable for some $1\le i<j\le d+1$. This answers a problem posed by Mardešić.

We present some related results on Boolean algebras not containing free products with too many uncountable factors. In particular, we answer a problem on initial chain algebras that was posed in [Order 14 (1997), pp. 21–38].

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Additional Information
  • Gonzalo Martínez-Cervantes
  • Affiliation: Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
  • Email: gonzalo.martinez2@um.es
  • Grzegorz Plebanek
  • Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • MR Author ID: 239421
  • Email: grzes@math.uni.wroc.pl
  • Received by editor(s): December 5, 2017
  • Received by editor(s) in revised form: December 9, 2017, and July 2, 2018
  • Published electronically: December 19, 2018
  • Additional Notes: The first author was partially supported by the research project 19275/PI/14 funded by Fundación Séneca – Agencia de Ciencia y Tecnología de la Región de Murcia within the framework of PCTIRM 2011-2014 and by Ministerio de Economía y Competitividad and FEDER (project MTM2014-54182-P)
    This research was done during the second’s author stay at Facultad de Matemáticas, Universidad de Murcia, supported by Fundación Séneca – Agencia de Ciencia y Tecnología de la Región de Murcia through its regional programme Jiménez de la Espada
  • Communicated by: Heike Mildenberger
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 1763-1772
  • MSC (2010): Primary 54F05, 54F45; Secondary 03G05, 06E15
  • DOI: https://doi.org/10.1090/proc/14313
  • MathSciNet review: 3910440