Topological groups: local versus global
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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1. Proper actions on topological groups: Applications to quotient spaces
Proceedings of the American Mathematical Society vol: 138 issue: 10 first page: 3707 year: 2010
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Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt