Theorems · Theorem · general topology
IsPreirreducible.image
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X},
IsPreirreducible s → ∀ (f : X → Y), ContinuousOn f s → IsPreirreducible (f '' s)- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement and proof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
- ContinuousOnstatement and proof · cited by 1,411
- Set.mem_image_of_memproof · cited by 371
- Set.inter_commproof · cited by 291
- Set.mem_preimageproof · cited by 190
- IsPreirreduciblestatement and proof · cited by 43
- Set.mem_of_mem_inter_leftproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- IsIrreducible.imageproof · cited by 7
- IsPreirreducible.of_subtypeproof · cited by 3
- Function.Surjective.preirreducibleSpaceproof · cited by 0