Theorems · Theorem · general topology
interior_iInter
∀ {ι : Sort u_1} {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] (f : ι → Set α),
interior (⋂ i, f i) = ⋂ i, interior (f i)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Set.iInterstatement · cited by 1,084
- interiorstatement · cited by 714
- interior_subsetproof · cited by 171
- isOpen_interiorproof · cited by 130
- LE.le.antisymm'proof · cited by 104
- AlexandrovDiscretestatement and proof · cited by 45
- Set.iInter_subsetproof · cited by 39
- interior_monoproof · cited by 38
- interior_maximalproof · cited by 29
- Set.subset_iInterproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- closure_iUnionproof · cited by 1
- interior_sInterproof · cited by 0