Theorems · Theorem · general topology
Set.Infinite.exists_accPt_of_subset_isCompact
∀ {X : Type u} [inst : TopologicalSpace X] {s K : Set X},
s.Infinite → IsCompact K → s ⊆ K → ∃ x ∈ K, AccPt x (Filter.principal s)- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsCompactstatement and proof · cited by 1,282
- Filter.principalstatement and proof · cited by 740
- Set.Infinitestatement and proof · cited by 263
- Filter.cofiniteproof · cited by 251
- inf_le_rightproof · cited by 238
- AccPtstatement and proof · cited by 75
- AccPt.monoproof · cited by 7
- Set.Infinite.exists_accPt_cofinite_inf_principal_of_subset_isCompactproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsCompact.finite_sdiff_of_mem_codiscreteWithinproof · cited by 2
- exists_nhds_ne_inf_principal_neBotproof · cited by 0