Theorems · Theorem · algebraic topology
IsEvenlyCovered.discreteTopology_fiber
∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} {I : Type u_3}
[inst_2 : TopologicalSpace I] {x : X}, IsEvenlyCovered f x I → DiscreteTopology ↑(f ⁻¹' {x})- Defined in
- Mathlib.Topology.Covering.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.preimagestatement · cited by 4,946
- DiscreteTopologystatement and proof · cited by 373
- IsEvenlyCoveredstatement and proof · cited by 22
- Homeomorph.discreteTopologyproof · cited by 5
- IsEvenlyCovered.fiberHomeomorphproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsCoveringMap.isSeparatedMapproof · cited by 4