Theorems · Theorem · general topology
LocallyFinite.point_finite
∀ {ι : Type u_1} {X : Type u_4} [inst : TopologicalSpace X] {f : ι → Set X},
LocallyFinite f → ∀ (x : X), {b | x ∈ f b}.Finite- Defined in
- Mathlib.Topology.LocallyFinite
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 65 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.
Cites9
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.ofPredstatement and proof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.Nonemptyproof · cited by 2,627
- Set.Finitestatement and proof · cited by 1,814
- Set.Finite.subsetproof · cited by 285
- LocallyFinitestatement and proof · cited by 141
- mem_of_mem_nhdsproof · cited by 126
Cited by9
Results whose statement or proof uses this declaration.
- SmoothBumpCovering.exists_isSubordinateproof · cited by 2
- PartitionOfUnity.le_oneproof · cited by 2
- BumpCovering.exists_isSubordinate_of_locallyFinite_of_propproof · cited by 2
- Metric.eventually_nhds_zero_forall_closedEBall_subsetproof · cited by 2
- IsOpen.exists_contMDiff_support_eqproof · cited by 1
- exists_locallyFinite_subset_iUnion_ball_radius_ltproof · cited by 1
- BumpCovering.point_finiteproof · cited by 1
- BumpCovering.exists_isSubordinate_of_locallyFinite_of_prop_t2spaceproof · cited by 1
- SmoothBumpCovering.point_finiteproof · cited by 0