Theorems · Theorem · functional analysis

ContinuousAlgEquiv.symm_map_nhds_eq

∀ {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) (a : A), Filter.map (⇑e.symm) (nhds (e a)) = nhds a

Defined in

Mathlib.Topology.Algebra.Algebra.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringTopologicalSpaceSemiringTopologicalSpaceAlgebraAlgebra