Theorems · Theorem · general topology
specializes_of_nhdsWithin
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {s : Set X}, nhdsWithin x s ≤ nhdsWithin y s → x ∈ s → x ⤳ y- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 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.
Cites10
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
- Filterstatement · cited by 8,121
- nhdsWithinstatement and proof · cited by 1,912
- inf_le_leftproof · cited by 286
- Specializesstatement · cited by 176
- le_infproof · cited by 107
- Filter.le_principal_iffproof · cited by 87
- pure_le_nhdsproof · cited by 39
- specializes_iff_pureproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- inseparable_of_nhdsWithin_eqproof · cited by 0