Theorems · Theorem · algebraic topology

ContinuousMap.HomotopyWith.trans_apply

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {P : C(X, Y) → Prop}
  {f₀ f₁ f₂ : C(X, Y)} (F : f₀.HomotopyWith f₁ P) (G : f₁.HomotopyWith f₂ P) (x : ↑unitInterval × X),
  (F.trans G) x = if h : ↑x.1 ≤ 1 / 2 then F (⟨2 * ↑x.1, ⋯⟩, x.2) else G (⟨2 * ↑x.1 - 1, ⋯⟩, x.2)

Defined in

Mathlib.Topology.Homotopy.Basic

Cited by

0 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace