Theorems · Theorem · general topology
interior_eq_iff_isOpen
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, interior s = s ↔ IsOpen s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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 · cited by 2,400
- interiorstatement and proof · cited by 714
- isOpen_interiorproof · cited by 130
- IsOpen.interior_eqproof · cited by 58
Cited by6
Results whose statement or proof uses this declaration.
- subset_interior_iff_isOpenproof · cited by 6
- isClopen_iff_frontier_eq_emptyproof · cited by 6
- Manifold.LiftSourceTargetPropertyAt.congr_of_eventuallyEqproof · cited by 3
- OpenPartialHomeomorph.symm_trans_restrproof · cited by 0
- OpenPartialHomeomorph.restr_inter_sourceproof · cited by 0
- OpenPartialHomeomorph.restr_symm_transproof · cited by 0