Theorems · Theorem · general topology
isOpen_setOfPred_eventually_nhdsWithin
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {p : X → Prop},
IsOpen {x | ∀ᶠ (y : X) in nhdsWithin x {x}ᶜ, p y}- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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.
Cites17
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
- Filterproof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement and proof · cited by 2,925
- IsOpenstatement · cited by 2,400
- nhdsWithinstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- eq_or_neproof · cited by 1,117
- T1Spacestatement and proof · cited by 275
Cited by2
Results whose statement or proof uses this declaration.
- isOpen_setOf_eventually_nhdsWithinproof · cited by 0
- MeromorphicAt.eventually_nhdsSet_eventuallyEq_codiscreteWithinproof · cited by 0