Theorems · Definition · algebraic topology

ContinuousMap.HomotopyEquiv.trans

{X : Type u} →
  {Y : Type v} →
    {Z : Type w} →
      [inst : TopologicalSpace X] →
        [inst_1 : TopologicalSpace Y] →
          [inst_2 : TopologicalSpace Z] →
            ContinuousMap.HomotopyEquiv X Y → ContinuousMap.HomotopyEquiv Y Z → ContinuousMap.HomotopyEquiv X Z

If X is homotopy equivalent to Y, and Y is homotopy equivalent to Z, then X is homotopy equivalent to Z.

Defined in

Mathlib.Topology.Homotopy.Equiv

Cited by

6 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace