Theorems · Theorem · field theory

affineHomeomorph_image_Ioc

∀ {𝕜 : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
  [inst_4 : IsTopologicalRing 𝕜] (a b c d : 𝕜) (h : 0 < a),
  ⇑(affineHomeomorph a b ⋯) '' Set.Ioc c d = Set.Ioc (a * c + b) (a * d + b)

Defined in

Mathlib.Topology.Algebra.Field

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingTopologicalSpaceIsTopologicalRing