Theorems · Theorem · general topology
continuous_from_compactlyGenerated
∀ {X : Type w} {Y : Type x} [inst : TopologicalSpace X] [t : TopologicalSpace Y] (f : X → Y),
(∀ (S : CompHaus) (g : C(↑S.toTop, X)), Continuous (f ∘ ⇑g)) → Continuous f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- TopCat.carrierstatement and proof · cited by 3,184
- Continuousstatement and proof · cited by 2,592
- ContinuousMapstatement and proof · cited by 2,491
- TopCatstatement · cited by 1,889
- CompHausLike.toTopstatement and proof · cited by 258
- CompHausstatement and proof · cited by 61
- continuous_coinduced_domproof · cited by 13
- TopologicalSpace.compactlyGeneratedstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- continuous_from_uCompactlyGeneratedSpaceproof · cited by 1