Finite products of limits of direct systems induced by maps

• Ivansic, Ivan ^[1] ; Rubin, Leonard R. ^[2]
  1. [1] University of Zagreb

     University of Zagreb

     Croacia

     
  2. [2] University of Oklahoma

     University of Oklahoma

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 2, 2015, págs. 209-215
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Let Z, H be spaces. In previous work, we introduced thedirect (inclusion) system induced by the set of maps between the spaces Z and H. Its direct limit is a subset of Z × H, but its topology is different from the relative topology. We found that many of the spaces constructed from this method are pseudo-compact and Tychonoff. We are going to show herein that these spaces are typically not sequentially compact and we will explore conditions under which a finite product of them will be pseudo-compact.