Theorems · Theorem · general topology
mem_interior
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {s : Set X}, x ∈ interior s ↔ ∃ t ⊆ s, IsOpen t ∧ x ∈ t- Defined in
- Mathlib.Topology.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsOpenstatement and proof · cited by 2,400
- interiorstatement · cited by 714
Cited by5
Results whose statement or proof uses this declaration.
- mem_interior_iff_mem_nhdsproof · cited by 82
- IsClosed.interior_union_leftproof · cited by 2
- MeasurableSet.of_mem_nhdsGT_auxproof · cited by 1
- IsUpperSet.mem_interior_of_forall_ltproof · cited by 1
- IsLowerSet.mem_interior_of_forall_ltproof · cited by 1