Theorems · Theorem · general topology
Dense.open_subset_closure_inter
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, Dense s → IsOpen t → t ⊆ closure (t ∩ s)- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 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.
Cites8
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 and proof · cited by 2,400
- closurestatement · cited by 1,254
- Densestatement and proof · cited by 359
- Set.inter_univproof · cited by 198
- Dense.closure_eqproof · cited by 24
- IsOpen.inter_closureproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Dense.isLUB_inter_iffproof · cited by 2
- DenseRange.subset_closure_image_preimage_of_isOpenproof · cited by 1