Theorems · Theorem · functional analysis

perfectSpace_of_module

∀ (𝕜 : Type u_1) (E : Type u_2) [inst : NontriviallyNormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [Nontrivial E] [inst_4 : TopologicalSpace E] [ContinuousAdd E] [ContinuousSMul 𝕜 E], PerfectSpace E

Defined in: Mathlib.Topology.Algebra.Module.PerfectSpace
Cited by: 0 results in Mathlib
Foundations: Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField AddCommGroup Module Nontrivial TopologicalSpace ContinuousAdd ContinuousSMul

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

TopologicalSpacestatement and proof · cited by 24,529
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
NontriviallyNormedFieldstatement and proof · cited by 8,742
nhdsproof · cited by 5,554
Norm.normproof · cited by 5,413
Set.univproof · cited by 3,945
Filter.Tendstoproof · cited by 3,814
Filter.Eventuallyproof · cited by 3,134
add_zeroproof · cited by 2,707
Nontrivialstatement and proof · cited by 2,416
Filter.atTopproof · cited by 2,405

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