Theorems · Theorem · complex analysis
isCoveringMap_zpow
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [ProperSpace 𝕜] (n : ℤ), ↑n ≠ 0 → IsCoveringMap fun x => ⟨↑x ^ n, ⋯⟩(· ^ n) : 𝕜 \ {0} → 𝕜 \ {0} is a covering map (if n ≠ 0 in 𝕜).
- Defined in
- Mathlib.Analysis.Complex.CoveringMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpaceproof · cited by 24,529
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Int.cast_natCastproof · cited by 393
- zpow_natCastproof · cited by 271
- Int.cast_negproof · cited by 224
- pow_ne_zeroproof · cited by 208
- zpow_negproof · cited by 198
- ProperSpacestatement and proof · cited by 190
- inv_powproof · cited by 140
- IsCoveringMapstatement and proof · cited by 68
- zpow_ne_zerostatement and proof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- isCoveringMapOn_zpowproof · cited by 0