Theorems · Theorem · general topology
Topology.IsInducing.indiscreteTopology
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace Y] [inst_1 : TopologicalSpace X] [IndiscreteTopology Y]
{f : X → Y}, Topology.IsInducing f → IndiscreteTopology X- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Top.topproof · cited by 9,680
- Topology.IsInducingstatement and proof · cited by 266
- IndiscreteTopologystatement and proof · cited by 43
- Topology.IsInducing.eq_inducedproof · cited by 31
- IndiscreteTopology.eq_topproof · cited by 4
- induced_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsInducing.nontrivialTopologyproof · cited by 1
- Homeomorph.indiscreteTopologyproof · cited by 1