A locally closed set with a smooth group structure is a Lie group
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- by Armando Machado PDF
- Proc. Amer. Math. Soc. 84 (1982), 303-307 Request permission
Abstract:
We prove the following result. Let $V$ be a smooth manifold and let $G \subset V$ be a locally closed set with a group structure such that both multiplication and inversion are smooth maps; then $G$ is an imbedded smooth submanifold of $V$. This result is a generalization of the well-known fact that a closed subgroup of a Lie group is itself a Lie group, because we are not assuming any group structure in the manifold $V$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 303-307
- MSC: Primary 22E15; Secondary 58A05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637188-2
- MathSciNet review: 637188