Theorems · Theorem · number theory
ZLattice.comap_discreteTopology
∀ (K : Type u_1) [inst : NormedField K] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace K E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace K F] (L : Submodule ℤ E)
[hL : DiscreteTopology ↥L] {e : F →ₗ[K] E},
Continuous ⇑e → Function.Injective ⇑e → DiscreteTopology ↥(ZLattice.comap K L e)- Defined in
- Mathlib.Algebra.Module.ZLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- LinearMapstatement and proof · cited by 10,215
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Continuousstatement and proof · cited by 2,592
- NormedFieldstatement and proof · cited by 1,084
- DiscreteTopologystatement and proof · cited by 373
- ZLattice.comapstatement · cited by 15
- DiscreteTopology.preimage_of_continuous_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ZLattice.exists_forall_abs_repr_le_normproof · cited by 2