Theorems · Theorem · general topology
isClosed_discrete
∀ {α : Type u_1} [inst : TopologicalSpace α] [DiscreteTopology α] (s : Set α), IsClosed s- Defined in
- Mathlib.Topology.Order
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 66 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Compl.complproof · cited by 2,925
- IsClosedstatement · cited by 1,639
- DiscreteTopologystatement and proof · cited by 373
- isOpen_discreteproof · cited by 36
Cited by9
Results whose statement or proof uses this declaration.
- isClopen_discreteproof · cited by 8
- Profinite.NobelingProof.isClosed_C1proof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- Profinite.NobelingProof.isClosed_C0proof · cited by 2
- Finset.rado_selectionproof · cited by 2
- IsClosed.two_pow_mk_le_two_pow_mk_denseproof · cited by 2
- closure_discreteproof · cited by 1
- PeriodPair.isClosed_of_subset_latticeproof · cited by 0