Theorems · Theorem · general topology
Complex.isOpen_re_lt_EReal
∀ (x : EReal), IsOpen {z | ↑z.re < x}An open left half-plane (with boundary real part given by an EReal) is an open set
in the complex plane.
- Defined in
- Mathlib.Analysis.Complex.HalfPlane
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement · cited by 6,101
- Complexstatement · cited by 5,565
- IsOpenstatement · cited by 2,400
- Complex.restatement · cited by 882
- ERealstatement and proof · cited by 793
- Real.toERealstatement · cited by 303
- continuous_constproof · cited by 278
- Complex.continuous_reproof · cited by 60
- isOpen_ltproof · cited by 23
- EReal.continuous_coe_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Complex.isOpen_re_ltproof · cited by 0