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Local topological group

A local topological group or local group is a topological space which behaves like a topological group sufficiently close to a distinguished identity element. topology Formally a local group consists of a topological space , open subets and , a distinguished identity element , and continuous functions and such that

1. and for all (identity)
2. if then (associativity)
3. with for all (inverse)

Hence needn’t be closed under .

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