Theorems · Theorem · general topology
iUnion_compactCovering
∀ (X : Type u_1) [inst : TopologicalSpace X] [inst_1 : SigmaCompactSpace X], ⋃ n, compactCovering X n = Set.univ
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.univstatement and proof · cited by 3,945
- Set.iUnionstatement and proof · cited by 2,483
- SigmaCompactSpacestatement and proof · cited by 55
- compactCoveringstatement · cited by 14
- Set.iUnion_accumulateproof · cited by 7
- SigmaCompactSpace.exists_compact_coveringproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- exists_mem_compactCoveringproof · cited by 3
- iUnion_closure_compactCoveringproof · cited by 2
- Topology.IsClosedEmbedding.sigmaCompactSpaceproof · cited by 1
- MeasureTheory.Measure.InnerRegularWRT.isCompact_isClosedproof · cited by 0
- MeasureTheory.Measure.finiteSpanningSetsInCompactproof · cited by 0
- LocallyFinite.countable_univproof · cited by 0