Analytic infinite gaps

• Antonio Avilés ; Stevo Todorcevic ^[1]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 40, Nº 2, 2025, págs. 143-158
• Idioma: inglés
• DOI: 10.17398/2605-5686.40.2.143
• Enlaces
  • Texto completo
• Resumen

  • We provide infinite-dimensional versions of analytic gap dichotomies, in the sense that a sequence of analytic hereditary families {Ip }p<ω of subsets of a countable set Ω is either countably separated or there is a tree structure inside Ω in which p-chains are sets from Ip . A topological version of this is that if K is a separable Rosenthal compact space, then either K is a continuous image of a finite-to-one preimage of a metric compactum or there is a tree structure inside K in which p-chains inside every branch form a relatively discrete family of sets

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