Theorems · Theorem · algebraic topology
isLocalHomeomorph_iff_isCoveringMap
∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} [T2Space E]
[T2Space X] [CompactSpace E], IsLocalHomeomorph f ↔ IsCoveringMap f- Defined in
- Mathlib.Topology.Covering.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Continuousproof · cited by 2,592
- T2Spacestatement and proof · cited by 1,351
- PartialEquiv.sourceproof · cited by 964
- PartialHomeomorph.toPartialEquivproof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphproof · cited by 851
- OpenPartialHomeomorph.toFun'proof · cited by 745
- OpenPartialHomeomorphproof · cited by 664
- CompactSpacestatement and proof · cited by 593
- continuous_iff_continuousAtproof · cited by 139
- IsCoveringMapstatement · cited by 68
- IsLocalHomeomorphstatement and proof · cited by 35
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.