Theorems · Theorem · Lie groups
IsCompact.locallyCompactSpace_of_mem_nhds_of_addGroup
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {K : Set G},
IsCompact K → ∀ {x : G}, K ∈ nhds x → LocallyCompactSpace G- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddproof · cited by 1,820
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- IsCompactstatement and proof · cited by 1,282
- neg_negproof · cited by 960
- LocallyCompactSpacestatement · cited by 324
- Continuous.continuousAtproof · cited by 297
- neg_add_revproof · cited by 236
Cited by5
Results whose statement or proof uses this declaration.
- isCompactOperator_id_iff_locallyCompactSpaceproof · cited by 3
- eq_zero_or_locallyCompactSpace_of_support_subset_isCompact_of_addGroupproof · cited by 2
- TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroupproof · cited by 2
- LocallyCompactSpace.of_locallyCompact_manifoldproof · cited by 1
- Valued.integer.properSpace_iff_compactSpace_integerproof · cited by 0