Theorems · Theorem · general topology

affineHomeomorph_image_I

∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
  [inst_4 : IsTopologicalRing 𝕜] (a b : 𝕜) (h : 0 < a), ⇑(affineHomeomorph a b ⋯) '' Set.Icc 0 1 = Set.Icc b (a + b)

The image of [0,1] under the homeomorphism fun x ↦ a * x + b is [b, a+b].

Defined in

Mathlib.Topology.UnitInterval

Cited by

0 results in Mathlib

Foundations

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

Assumes

FieldLinearOrderIsStrictOrderedRingTopologicalSpaceIsTopologicalRing