Theorems · Theorem · general topology
specializes_iff_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {x y : X}, x ⤳ y ↔ x = y- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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.
- TopologicalSpacestatement and proof · cited by 24,529
- T1Spacestatement and proof · cited by 275
- Specializesstatement · cited by 176
- Specializes.eqproof · cited by 4
- specializes_rflproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- pure_le_nhds_iffproof · cited by 3
- specializes_eq_eqproof · cited by 2
- IsDiscrete.eq_of_specializesproof · cited by 1
- nhds_le_nhds_iffproof · cited by 0