Theorems · Theorem · general topology
IsOpen.preimage_val
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsOpen t → IsOpen (Subtype.val ⁻¹' t)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 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.
Cites7
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.Elemstatement · cited by 7,166
- Set.preimagestatement · cited by 4,946
- IsOpenstatement and proof · cited by 2,400
- continuous_subtype_valproof · cited by 159
- IsOpen.preimageproof · cited by 147
Cited by4
Results whose statement or proof uses this declaration.
- exists_open_dense_of_open_dense_subtypeproof · cited by 1
- IsOpen.inter_preimage_val_iffproof · cited by 0
- IsOpen.smul_sphereproof · cited by 0
- CompactCoherentification.isOpenMap_mkproof · cited by 0