Theorems · Theorem · general topology
closure_discrete
∀ {α : Type u_1} [inst : TopologicalSpace α] [DiscreteTopology α] (s : Set α), closure s = s- Defined in
- Mathlib.Topology.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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
- closurestatement · cited by 1,254
- DiscreteTopologystatement and proof · cited by 373
- IsClosed.closure_eqproof · cited by 139
- isClosed_discreteproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- DenselyOrdered.subsingleton_of_discreteTopologyproof · cited by 0