Theorems · Theorem · operator theory
isCompactOperator_id_iff_locallyCompactSpace
∀ {E : Type u_1} [inst : AddGroup E] [inst_1 : TopologicalSpace E] [IsTopologicalAddGroup E],
IsCompactOperator id ↔ LocallyCompactSpace E- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- IsCompactproof · cited by 1,282
- LocallyCompactSpacestatement and proof · cited by 324
- IsCompactOperatorstatement and proof · cited by 51
- WeaklyLocallyCompactSpace.exists_compact_mem_nhdsproof · cited by 28
- IsCompact.locallyCompactSpace_of_mem_nhds_of_addGroupproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- isCompactOperator_idproof · cited by 2
- LocallyCompactSpace.of_isCompactOperator_idproof · cited by 2
- isCompactOperator_id_iff_finiteDimensionalproof · cited by 1