Theorems · Theorem · algebraic topology

ContinuousMap.homotopic_const_iff

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x₀ x₁ : X} [Nonempty Y],
  (ContinuousMap.const Y x₀).Homotopic (ContinuousMap.const Y x₁) ↔ Joined x₀ x₁

Two constant continuous maps with nonempty domain are homotopic if and only if their values are joined by a path in the codomain.

Defined in

Mathlib.Topology.Homotopy.Path

Cited by

0 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceNonempty