Theorems · Theorem · functional analysis

ContinuousLinearEquiv.isClosed_image

∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁}
  [inst_2 : RingHomInvPair σ₁₂ σ₂₁] [inst_3 : RingHomInvPair σ₂₁ σ₁₂] {M₁ : Type u_4} [inst_4 : TopologicalSpace M₁]
  [inst_5 : AddCommMonoid M₁] {M₂ : Type u_5} [inst_6 : TopologicalSpace M₂] [inst_7 : AddCommMonoid M₂]
  [inst_8 : Module R₁ M₁] [inst_9 : Module R₂ M₂] (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁}, IsClosed (⇑e '' s) ↔ IsClosed s

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule