Theorems · Theorem · general topology
discreteTopology_iff_singleton_mem_nhds
∀ {α : Type u_1} [inst : TopologicalSpace α], DiscreteTopology α ↔ ∀ (x : α), {x} ∈ nhds x- Defined in
- Mathlib.Topology.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- DiscreteTopologystatement · cited by 373
Cited by3
Results whose statement or proof uses this declaration.
- Summable.hasFiniteSupport_of_discreteTopologyproof · cited by 2
- Multipliable.hasFiniteMulSupport_of_discreteTopologyproof · cited by 1
- discreteTopology_iff_locallyInjectiveproof · cited by 0