Theorems · Theorem · general topology
isOpen_setOf_eventually_nhdsWithin
Deprecated since 2026-07-09Use isOpen_setOfPred_eventually_nhdsWithin instead.
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {p : X → Prop},
IsOpen {x | ∀ᶠ (y : X) in nhdsWithin x {x}ᶜ, p y}Alias of isOpen_setOfPred_eventually_nhdsWithin.
- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- Set.ofPredstatement · cited by 6,101
- Filter.Eventuallystatement · cited by 3,134
- Compl.complstatement · cited by 2,925
- IsOpenstatement · cited by 2,400
- nhdsWithinstatement · cited by 1,912
- T1Spacestatement · cited by 275
- isOpen_setOfPred_eventually_nhdsWithinproof · cited by 2
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