Theorems · Theorem · Lie groups
TopologicalGroup.IsSES.ofClosedSubgroup
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] (H : Subgroup G)
[inst_3 : H.Normal], IsClosed ↑H → TopologicalGroup.IsSES H.subtype (QuotientGroup.mk' H)Construct a short exact sequence of topological groups from a closed normal subgroup.
- Defined in
- Mathlib.Topology.Algebra.Group.Extension
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- IsClosedstatement and proof · cited by 1,639
- IsTopologicalGroupstatement and proof · cited by 469
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.subtypestatement · cited by 185
- Subtype.range_coe_subtypeproof · cited by 170
- QuotientGroup.mk'statement · cited by 90
- Topology.IsInducing.subtypeValproof · cited by 43
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