Theorems · Theorem · general topology
Complex.frontier_preimage_im
∀ (s : Set ℝ), frontier (Complex.im ⁻¹' s) = Complex.im ⁻¹' frontier s
- Defined in
- Mathlib.Analysis.Complex.ReImTopology
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Set.preimagestatement · cited by 4,946
- Complex.imstatement · cited by 591
- frontierstatement · cited by 214
- Complex.continuous_improof · cited by 32
- IsOpenMap.preimage_frontier_eq_frontier_preimageproof · cited by 6
- Complex.isOpenMap_improof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Complex.frontier_setOfPred_im_leproof · cited by 1
- Complex.frontier_setOfPred_im_ltproof · cited by 1
- Complex.frontier_setOfPred_le_improof · cited by 1
- Complex.frontier_setOfPred_lt_improof · cited by 1