Theorems · Theorem · general topology
interior_interior
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, interior (interior s) = interior s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 8 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.
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
- interiorstatement · cited by 714
- isOpen_interiorproof · cited by 130
- IsOpen.interior_eqproof · cited by 58
Cited by8
Results whose statement or proof uses this declaration.
- strictConcaveOn_of_deriv2_negproof · cited by 4
- strictConvexOn_of_deriv2_posproof · cited by 2
- concaveOn_of_deriv2_nonposproof · cited by 2
- convexOn_of_deriv2_nonnegproof · cited by 2
- ContinuousOn.continuousAt_indicatorproof · cited by 1
- frontier_interior_subsetproof · cited by 1
- OpenPartialHomeomorph.restr_eqOnSource_of_eqOnproof · cited by 1
- ContinuousOn.continuousAt_mulIndicatorproof · cited by 0