Theorems · Theorem · functional analysis
ContinuousLinearEquiv.nhds
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : SeminormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
[CompleteSpace E] (e : E ≃L[𝕜] F), Set.range ContinuousLinearEquiv.toContinuousLinearMap ∈ nhds ↑e- Cited by
- 2 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- ContinuousLinearMapstatement · cited by 5,352
- Set.rangestatement · cited by 4,705
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousLinearEquivstatement and proof · cited by 743
Cited by2
Results whose statement or proof uses this declaration.
- exists_continuousLinearEquiv_fderivWithin_symm_eqproof · cited by 3
- OpenPartialHomeomorph.contDiffAt_symmproof · cited by 3