Theorems · Theorem · general topology
Continuous.specialization_monotone
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Continuous f → Monotone fA continuous function is monotone with respect to the specialization preorders on the domain and the codomain.
- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- Monotonestatement · cited by 1,397
- Specializes.mapproof · cited by 19
- specializationPreorderstatement · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- specializingMap_iff_closure_singletonproof · cited by 1
- StableUnderGeneralization.preimageproof · cited by 0
- StableUnderSpecialization.preimageproof · cited by 0