Mathlib Map

Theorems · Theorem · general topology

Topology.IsInducing.nontrivialTopology

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace Y] [inst_1 : TopologicalSpace X] [NontrivialTopology X]
  {f : X → Y}, Topology.IsInducing f → NontrivialTopology Y
Defined in
Mathlib.Topology.Maps.Basic
Cited by
1 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceNontrivialTopology
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Homeomorph.nontrivialTopology · cited by 1Homeomorph.nontrivialTopo…TopologicalSpace · cited by 24529TopologicalSpaceTopology.IsInducing · cited by 266Topology.IsInducingnot_imp_not · cited by 63not_imp_notNontrivialTopology · cited by 46NontrivialTopologyIndiscreteTopology · cited by 43IndiscreteTopologyTopology.IsInducing.indiscreteTopology · cited by 2IsInducing.indiscreteTopo…IsInducing.nontrivialTopologyCITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.