Pettis property for Polish inverse semigroups

• Arana, Karen ; Pérez, Jerson ; Uzcátegui, Carlos ^[1]
  1. [1] Universidad Industrial de Santander

     Universidad Industrial de Santander

     Colombia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 2, 2023, págs. 455-467
• Idioma: inglés
• DOI: 10.4995/agt.2023.17396
• Enlaces
  • Texto completo
• Resumen
  • español

    Estudiamos una propiedad de semigrupos inversos polacos análoga al teorema clásico de Pettis sobre grupos polacos. A diferencia de lo que ocurre con los grupos, mostramos que no todo semigrupo inverso polaco tiene la propiedad de Pettis. Presentamos varios ejemplos de subsemigrupos inversos polacos del semigrupo inverso simátrico I(N) que consiste de todas las biyecciones parciales entre subconjuntos de N. También estudiaremos si esos semigrupos poseen la propiedad de continuidad automática.

  • English

    We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.

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