Theorems · Theorem · general topology
Topology.IsInducing.specializes_iff
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x y : X} {f : X → Y},
Topology.IsInducing f → (f x ⤳ f y ↔ x ⤳ y)- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 10 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- closureproof · cited by 1,254
- Topology.IsInducingstatement and proof · cited by 266
- Specializesstatement · cited by 176
- Set.image_singletonproof · cited by 174
- Topology.IsInducing.closure_eq_preimage_closure_imageproof · cited by 11
Cited by10
Results whose statement or proof uses this declaration.
- Topology.IsInducing.inseparable_iffproof · cited by 6
- IsDiscrete.eq_of_specializesproof · cited by 1
- subtype_specializes_iffproof · cited by 1
- Topology.IsInducing.generalizingMapproof · cited by 1
- Topology.IsInducing.r1Spaceproof · cited by 1
- Topology.IsInducing.joinedIn_imageproof · cited by 1
- Topology.IsInducing.specializingMapproof · cited by 0
- SeparationQuotient.t1Space_iffproof · cited by 0
- OnePoint.specializes_coeproof · cited by 0
- Topology.IsInducing.r0Spaceproof · cited by 0