Theorems · Theorem · general topology
subset_interior_iff_isOpen
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, s ⊆ interior s ↔ IsOpen s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 64 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.
Cites5
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
- interior_eq_iff_isOpenproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- isOpen_iff_forall_mem_openproof · cited by 18
- isOpen_iff_nhdsproof · cited by 6
- isOpen_singleton_of_finite_mem_nhdsproof · cited by 2
- isOpenMap_iff_image_interiorproof · cited by 1
- continuous_iff_preimage_interior_subset_interior_preimageproof · cited by 0
- Metric.thickening_subset_interior_cthickeningproof · cited by 0