Theorems · Theorem · general topology
Topology.IsCoinducing.continuous
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsCoinducing f → Continuous f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Continuousstatement · cited by 2,592
- IsOpenproof · cited by 2,400
- Topology.IsCoinducingstatement and proof · cited by 31
- Topology.IsCoinducing.isOpen_preimageproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- Topology.IsCoinducing.connectedComponentsHomeomorphproof · cited by 3
- Topology.IsCoinducing.preimage_connectedComponentproof · cited by 2
- Topology.IsCoinducing.restrictPreimage_of_isOpenproof · cited by 1
- Topology.IsCoinducing.locallyConnectedSpaceproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.connectedComponentsHomeomorph_applystatement · cited by 0
- Topology.IsCoinducing.connectedComponentsMapstatement · cited by 0
- Topology.IsCoinducing.connectedComponentsMap_bijectivestatement and proof · cited by 0