Theorems · Theorem · functional analysis
NormedRing.inverse_continuousAt
∀ {R : Type u_1} [inst : NormedRing R] [HasSummableGeomSeries R] (x : Rˣ), ContinuousAt Ring.inverse ↑xThe function Ring.inverse is continuous at each unit of R.
- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 3 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- NormedRingstatement and proof · cited by 924
- one_ne_zeroproof · cited by 885
- ContinuousAtstatement · cited by 697
- div_oneproof · cited by 629
- Filter.Tendsto.compproof · cited by 560
- Asymptotics.IsLittleOproof · cited by 375
- add_sub_cancelproof · cited by 195
Cited by3
Results whose statement or proof uses this declaration.
- Units.isOpenEmbedding_valproof · cited by 2
- Subalgebra.isUnit_of_isUnit_val_of_eventuallyproof · cited by 1
- ContinuousMap.continuous_isUnit_unitproof · cited by 0