Theorems · Theorem · general topology
DiscreteTopology.of_finite_of_isClosed_singleton
∀ {α : Type u_1} [inst : TopologicalSpace α] [Finite α], (∀ (a : α), IsClosed {a}) → DiscreteTopology α- Defined in
- Mathlib.Topology.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceFinite
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.Elemproof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- IsClosedstatement and proof · cited by 1,639
- DiscreteTopologystatement · cited by 373
- isClosed_iUnion_of_finiteproof · cited by 6
- Set.iUnion_of_singleton_coeproof · cited by 6
- discreteTopology_iff_forall_isClosedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.discreteTopology_iff_finite_and_krullDimLE_zeroproof · cited by 3