Partial actions of groups on profinite spaces

• Martínez, Luis ^[1] ; Pinedo, Héctor ^[2] ; Villamizar, Andrés ^[3]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
  2. [2] Universidad Industrial de Santander

     Universidad Industrial de Santander

     Colombia

     
  3. [3] Universidad de Pamplona

     Universidad de Pamplona

     Colombia

     

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 143-157
• Idioma: inglés
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• Resumen

  • We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG  : X → X / ∼G  of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.