Theorems · Theorem · general topology

ContinuousMap.comp_attachBound_mem_closure

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : CompactSpace X] (A : Subalgebra ℝ C(X, ℝ)) (f : ↥A)
  (p : C(↑(Set.Icc (-‖f‖) ‖f‖), ℝ)), p.comp (↑f).attachBound ∈ A.topologicalClosure

Defined in

Mathlib.Topology.ContinuousMap.StoneWeierstrass

Cited by

1 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCompactSpace