Theorems · Inductive type · general topology
CompactExhaustion
(X : Type u_4) → [TopologicalSpace X] → Type u_4
An [exhaustion by compact sets](https://en.wikipedia.org/wiki/Exhaustion_by_compact_sets) of a
topological space is a sequence of compact sets K n such that K n ⊆ interior (K (n + 1)) and
⋃ n, K n = univ.
If X is a locally compact sigma compact space, then CompactExhaustion.choice X provides
a choice of an exhaustion by compact sets. This choice is also available as
(default : CompactExhaustion X).
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by35
Results whose statement or proof uses this declaration.
- CompactExhaustion.subsetstatement and proof · cited by 7
- CompactExhaustion.findstatement and proof · cited by 6
- CompactExhaustion.exists_memstatement and proof · cited by 5
- CompactExhaustion.isCompactstatement and proof · cited by 4
- CompactExhaustion.shiftrstatement and proof · cited by 4
- CompactExhaustion.subset_interior_succstatement and proof · cited by 4
- CompactExhaustion.toFunstatement and proof · cited by 4
- refinement_of_locallyCompact_sigmaCompact_of_nhds_basis_setproof · cited by 3
- CompactExhaustion.exists_superset_of_isCompactstatement and proof · cited by 2
- CompactExhaustion.find_shiftrstatement and proof · cited by 2
- CompactExhaustion.mem_findstatement and proof · cited by 2
- CompactExhaustion.mem_sdiff_shiftr_findstatement and proof · cited by 2