Theorems · Theorem · general topology
Set.Finite.isClosed
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s : Set X}, s.Finite → IsClosed s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Finitestatement and proof · cited by 1,814
- IsClosedstatement and proof · cited by 1,639
- T1Spacestatement and proof · cited by 275
- isClosed_singletonproof · cited by 66
- Set.biUnion_of_singletonproof · cited by 43
- Set.Finite.isClosed_biUnionproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- t1Space_TFAEproof · cited by 8
- EReal.continuous_toENNRealproof · cited by 4
- nhdsNE_of_nhdsNE_sdiff_finiteproof · cited by 3
- codiscrete_le_cofiniteproof · cited by 2
- isOpen_singleton_of_finite_mem_nhdsproof · cited by 2
- Finset.isClosedproof · cited by 0