Theorems · Inductive type · general topology
R0Space
(X : Type u) → [TopologicalSpace X] → Prop
A topological space is called an R₀ space, if Specializes relation is symmetric.
In other words, given two points x y : X,
if every neighborhood of y contains x, then every neighborhood of x contains y.
- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by25
Results whose statement or proof uses this declaration.
- t1Space_TFAEstatement and proof · cited by 8
- specializes_iff_inseparablestatement and proof · cited by 5
- Specializes.symmstatement and proof · cited by 4
- t1Space_iff_specializes_imp_eqproof · cited by 4
- specializes_commstatement and proof · cited by 3
- Bornology.relativelyCompactstatement and proof · cited by 3
- t1Space_iff_exists_openproof · cited by 3
- R0Space.closure_singletonstatement and proof · cited by 2
- Bornology.relativelyCompact.isBounded_iffstatement and proof · cited by 1
- R0Space.casesOnstatement and proof · cited by 1
- R0Space.specializes_symmstatement and proof · cited by 1
- WithSeminorms.separating_of_T1proof · cited by 1