Theorems · Theorem · functional analysis
Ideal.closure_ne_top
∀ {R : Type u_1} [inst : NormedRing R] [HasSummableGeomSeries R] (I : Ideal R), I ≠ ⊤ → I.closure ≠ ⊤The Ideal.closure of a proper ideal in a normed ring with summable
geometric series is proper.
- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- closureproof · cited by 1,254
- NormedRingstatement and proof · cited by 924
- closure_minimalproof · cited by 94
- HasSummableGeomSeriesstatement and proof · cited by 60
- Ideal.eq_top_iff_oneproof · cited by 56
- nonunitsproof · cited by 35
- Ideal.closurestatement and proof · cited by 8
- coe_subset_nonunitsproof · cited by 2
- nonunits.isClosedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.IsMaximal.closure_eqproof · cited by 0