Theorems · Theorem · general topology
continuous_rangeFactorization_iff
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Continuous (Set.rangeFactorization f) ↔ Continuous f- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Continuousstatement · cited by 2,592
- Set.rangeFactorizationstatement · cited by 56
- Topology.IsInducing.subtypeValproof · cited by 43
- Topology.IsInducing.continuous_iffproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- Continuous.rangeFactorizationproof · cited by 3
- Topology.IsStrictMap.continuousproof · cited by 0