Topological groups: local versus global


  • A. V. Arhangelskii Ohio University
  • Vladimir V. Uspenskij Ohio University



Topological group, Paracompact, Lindelöf, Local properties


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.


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Author Biographies

A. V. Arhangelskii, Ohio University

Department of Mathematics

Vladimir V. Uspenskij, Ohio University

Department of Mathematics


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How to Cite

A. V. Arhangelskii and V. V. Uspenskij, “Topological groups: local versus global”, Appl. Gen. Topol., vol. 7, no. 1, pp. 67–72, Apr. 2006.