Topological groups: local versus global

Abstract

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.

Keywords

• Topological group
• Paracompact
• Lindelöf
• Local properties