Theorems · Definition · general topology
compactCovering
(X : Type u_1) → [inst : TopologicalSpace X] → [SigmaCompactSpace X] → ℕ → Set X
A choice of compact covering for a σ-compact space, chosen to be monotone.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SigmaCompactSpacestatement and proof · cited by 55
- Set.accumulateproof · cited by 32
- SigmaCompactSpace.exists_compact_coveringproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- isCompact_compactCoveringstatement · cited by 8
- iUnion_compactCoveringstatement · cited by 5
- exists_mem_compactCoveringstatement · cited by 3
- iUnion_closure_compactCoveringstatement · cited by 2
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_isCompact_eq_zeroproof · cited by 1
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_isCompact_eq_zero'proof · cited by 1
- vadd_singleton_mem_nhds_of_sigmaCompactproof · cited by 1
- smul_singleton_mem_nhds_of_sigmaCompactproof · cited by 1
- countable_cover_nhdsWithin_of_sigmaCompactproof · cited by 1
- Topology.IsClosedEmbedding.sigmaCompactSpaceproof · cited by 1
- compactCovering_subsetstatement · cited by 1
- MeasureTheory.Measure.finiteSpanningSetsInCompactproof · cited by 0