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Closed-subgroup theorem

In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H is a closed subgroup of a Lie group G, then H is an embedded Lie group with the smooth structure (and hence the group topology) agreeing with the embedding. One of several results known as Cartan's theorem…

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Example of a non-closed subgroup

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Conditions for being closed

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Closed-subgroup theorem

Nodes50
Edges49
Triples0
Avg. degree1.96
Density0.04
Components1

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closed lie subgroup group displaystyle theorem mathfrak topology embedded neighborhood identity since one algebra relative analytic groups proof left exponential

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