Theorems · Theorem · general topology
IsClosed.interior_union_left
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsClosed s → interior (s ∪ t) ⊆ s ∪ interior t- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 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.
Cites9
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
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- IsClosedstatement and proof · cited by 1,639
- interiorstatement and proof · cited by 714
- IsClosed.isOpen_complproof · cited by 126
- IsOpen.interproof · cited by 98
- mem_interiorproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsOpen.inter_closureproof · cited by 8
- IsClosed.interior_union_rightproof · cited by 0