Theorems · Theorem · general topology
Topology.IsQuotientMap.continuous_iff
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {f : X → Y} {g : Y → Z} [inst : TopologicalSpace X]
[inst_1 : TopologicalSpace Y] [inst_2 : TopologicalSpace Z],
Topology.IsQuotientMap f → (Continuous g ↔ Continuous (g ∘ f))- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- Topology.IsQuotientMapstatement and proof · cited by 124
- TopologicalSpace.coinducedproof · cited by 56
- Topology.IsQuotientMap.isCoinducingproof · cited by 35
- continuous_iff_coinduced_leproof · cited by 13
- Topology.IsCoinducing.eq_coinducedproof · cited by 9
- coinduced_composeproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Topology.IsQuotientMap.continuousproof · cited by 14
- Homeomorph.comp_continuous_iff'proof · cited by 4
- Topology.IsGeneratedBy.continuous_iffproof · cited by 3
- IsModuleTopology.continuous_bilinear_of_finite_leftproof · cited by 2
- IsOpenQuotientMap.continuous_comp_iffproof · cited by 1
- Topology.IsQuotientMap.continuous_lift_prod_leftproof · cited by 1
- Submodule.IsCompl.isTopCompl_iff_continuous_quotientEquivOfIsComplproof · cited by 0
- Topology.IsQuotientMap.continuousOn_isOpen_iffproof · cited by 0
- IsOpenQuotientMap.of_comp_iffproof · cited by 0
- continuous_IccExtend_iffproof · cited by 0