Theorems · Theorem · functional analysis
nonunits.isClosed
∀ {R : Type u_1} [inst : NormedRing R] [HasSummableGeomSeries R], IsClosed (nonunits R)- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsClosedstatement · cited by 1,639
- NormedRingstatement and proof · cited by 924
- HasSummableGeomSeriesstatement and proof · cited by 60
- IsOpen.isClosed_complproof · cited by 50
- nonunitsstatement · cited by 35
- Units.isOpenproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- upperHemicontinuous_spectrumproof · cited by 4
- Ideal.closure_ne_topproof · cited by 1