Topological groups: local versus global

A. V. Arhangelskii, Vladimir V. Uspenskij


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.


Topological group; Paracompact; Lindelöf; Local properties

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doi: 10.1090/S0002-9939-2010-10504-X

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Universitat Politècnica de València

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