Theorems · Theorem · general topology
interior_inter
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, interior (s ∩ t) = interior s ∩ interior t- Defined in
- Mathlib.Topology.Closure
- Cited by
- 22 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.
Cites11
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
- LE.le.antisymmproof · cited by 507
- interior_subsetproof · cited by 171
- isOpen_interiorproof · cited by 130
- IsOpen.interproof · cited by 98
- Set.inter_subset_interproof · cited by 66
- interior_monoproof · cited by 38
- interior_maximalproof · cited by 29
- Monotone.map_inf_leproof · cited by 19
Cited by22
Results whose statement or proof uses this declaration.
- interior_Iccproof · cited by 37
- closure_unionproof · cited by 13
- interior_Icoproof · cited by 12
- interior_Iocproof · cited by 10
- Set.Finite.interior_biInterproof · cited by 5
- OpenPartialHomeomorph.restr_source_interproof · cited by 4
- extChartAt_mem_closure_interiorproof · cited by 2
- ModelWithCorners.isInteriorPoint_iff_isInteriorPoint_valproof · cited by 2
- OpenPartialHomeomorph.mem_interior_extend_targetproof · cited by 2
- interior_union_inter_interior_compl_left_subsetproof · cited by 1
- interior_union_inter_interior_compl_right_subsetproof · cited by 1
- Complex.interior_reProdImproof · cited by 1