Mathlib Map

Theorems · Theorem · functional analysis

Units.isOpenMap_val

∀ {R : Type u_1} [inst : NormedRing R] [HasSummableGeomSeries R], IsOpenMap Units.val

In a normed ring with summable geometric series, the coercion from Rˣ (equipped with the induced topology from the embedding in R × R) to R is an open map.

Defined in
Mathlib.Analysis.Normed.Ring.Units
Cited by
0 results in Mathlib
Foundations
Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedRingHasSummableGeomSeries
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Units · cited by 2804UnitsUnits.val · cited by 1966Units.valNormedRing · cited by 924NormedRingIsOpenMap · cited by 253IsOpenMapHasSummableGeomSeries · cited by 60HasSummableGeomSeriesTopology.IsOpenEmbedding.isOpenMap · cited by 50IsOpenEmbedding.isOpenMapUnits.isOpenEmbedding_val · cited by 2Units.isOpenEmbedding_valUnits.isOpenMap_valCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.