Mathlib Map

Theorems · Theorem · general topology

t1Space_of_injective_of_continuous

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Function.Injective f → Continuous f → ∀ [T1Space Y], T1Space X
Defined in
Mathlib.Topology.Separation.Basic
Cited by
2 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceT1Space
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Topology.IsEmbedding.t1Space · cited by 3IsEmbedding.t1Spacet5Space_iff_forall_isOpen_t4Space · cited by 2t5Space_iff_forall_isOpen…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousT1Space · cited by 275T1SpaceSpecializes · cited by 176SpecializesSpecializes.map · cited by 19Specializes.mapt1Space_iff_specializes_imp_eq · cited by 4t1Space_iff_specializes_i…Specializes.eq · cited by 4Specializes.eqt1Space_of_injective_of_conti…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.