Theorems · Theorem · general topology
ContinuousMap.isUnit_iff_forall_isUnit
∀ {X : Type u_1} {R : Type u_3} [inst : TopologicalSpace X] [inst_1 : NormedRing R] [CompleteSpace R] (f : C(X, R)),
IsUnit f ↔ ∀ (x : X), IsUnit (f x)- Defined in
- Mathlib.Topology.ContinuousMap.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Equiv.symmproof · cited by 3,681
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMapstatement and proof · cited by 2,491
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- NormedRingstatement and proof · cited by 924
- IsUnit.unitproof · cited by 252
- ContinuousMap.extproof · cited by 92
- ContinuousMap.unitsLiftproof · cited by 5
- ContinuousMap.unitsOfForallIsUnitproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.isUnit_iff_forall_ne_zeroproof · cited by 0