Theorems · Theorem · functional analysis

NonUnitalStarSubalgebra.topologicalClosure_map_le

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : TopologicalSpace A] [inst_2 : Star A]
  [inst_3 : NonUnitalSemiring A] [inst_4 : Module R A] [inst_5 : ContinuousStar A] [inst_6 : ContinuousConstSMul R A]
  [inst_7 : IsSemitopologicalSemiring A] [inst_8 : TopologicalSpace B] [inst_9 : Star B] [inst_10 : NonUnitalSemiring B]
  [inst_11 : Module R B] [inst_12 : IsSemitopologicalSemiring B] [inst_13 : ContinuousConstSMul R B]
  [inst_14 : ContinuousStar B] (s : NonUnitalStarSubalgebra R A) {φ : A →⋆ₙₐ[R] B},
  IsClosedMap ⇑φ →
    (NonUnitalStarSubalgebra.map φ s).topologicalClosure ≤ NonUnitalStarSubalgebra.map φ s.topologicalClosure

Defined in

Mathlib.Topology.Algebra.NonUnitalStarAlgebra

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringTopologicalSpaceStarNonUnitalSemiringModuleContinuousStarContinuousConstSMulIsSemitopologicalSemiringTopologicalSpaceStarNonUnitalSemiringModuleIsSemitopologicalSemiringContinuousConstSMulContinuousStar