Topological groups: local versus global

• Arhangelskii, A.V. ^[1] ; Uspenskij, Vladimir V. ^[1]
  1. [1] Ohio University

     Ohio University

     Township of Athens, Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 7, Nº. 1, 2006, págs. 67-72
• Idioma: inglés
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• Resumen

  • It is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement using quotients. Similar ‘local implies global’ theorems hold also for many other properties, such as normality, metacompactness, stratifiability, etc.