Theorems · Theorem · general topology
tendsto_residual_of_isOpenMap
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
Continuous f → IsOpenMap f → Filter.Tendsto f (residual α) (residual β)- Defined in
- Mathlib.Topology.Baire.BaireMeasurable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- Filter.Tendstostatement · cited by 3,814
- Continuousstatement and proof · cited by 2,592
- IsOpenproof · cited by 2,400
- Denseproof · cited by 359
- IsOpenMapstatement and proof · cited by 253
- IsOpen.preimageproof · cited by 147
- residualstatement · cited by 23
- Dense.preimageproof · cited by 8
- residual_of_dense_openproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsMeagre.preimage_of_isOpenMapproof · cited by 0
- BaireMeasurableSet.preimageproof · cited by 0
- Homeomorph.residual_map_eqproof · cited by 0