Theorems · Theorem · functional analysis

ContinuousAlgEquiv.isClosed_image

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : TopologicalSpace A] [inst_3 : Semiring B] [inst_4 : TopologicalSpace B] [inst_5 : Algebra R A]
  [inst_6 : Algebra R B] (e : A ≃A[R] B) {S : Set A}, IsClosed (⇑e '' S) ↔ IsClosed S

Defined in

Mathlib.Topology.Algebra.Algebra.Equiv

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringTopologicalSpaceSemiringTopologicalSpaceAlgebraAlgebra