Disconnection in the Alexandroff duplicate

• Bhattacharjee, Papiya ^[1] ; Knox, Michelle L. ^[2] ; McGovern, Warren Wm. ^[1]
  1. [1] Florida Atlantic University

     Florida Atlantic University

     Estados Unidos

     
  2. [2] Midwestern State University

     Midwestern State University

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 331-344
• Idioma: inglés
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• Resumen

  • It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.