Theorems · Theorem · general topology
exists_mem_compactCovering
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : SigmaCompactSpace X] (x : X), ∃ n, x ∈ compactCovering X n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.iUnion_eq_univ_iffproof · cited by 19
- compactCoveringstatement · cited by 14
- iUnion_compactCoveringproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- smul_singleton_mem_nhds_of_sigmaCompactproof · cited by 1
- countable_cover_nhdsWithin_of_sigmaCompactproof · cited by 1
- vadd_singleton_mem_nhds_of_sigmaCompactproof · cited by 1