Theorems · Theorem · general topology
Specializes.map
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x y : X} {f : X → Y},
x ⤳ y → Continuous f → f x ⤳ f y- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 78 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
- Continuous.continuousAtproof · cited by 297
- Specializesstatement and proof · cited by 176
- Specializes.map_of_continuousAtproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- ContinuousMap.map_specializesproof · cited by 13
- Continuous.specialization_monotoneproof · cited by 3
- t1Space_of_injective_of_continuousproof · cited by 2
- Specializes.negproof · cited by 1
- Specializes.smulproof · cited by 1
- Specializes.vaddproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1
- GeneralizingMap.restrictPreimageproof · cited by 1
- norm_image_of_norm_eq_zeroproof · cited by 1
- Specializes.invproof · cited by 1
- Seminorm.map_eq_zero_of_norm_eq_zeroproof · cited by 1
- AlgebraicGeometry.Scheme.range_fromSpecStalkproof · cited by 0