Topic: Homotopy of Maps and Paths

Homotopies Relative to a Subspace

Homotopic Maps as an Equivalence Relation

Homotopies of Concatenated Paths

Homeomorphism Versus Homotopy Equivalence

Explicit Contractions of Convex and Star-Shaped Sets

Deformation Retracts and Strong Deformation Retracts

Deformation Retraction of a Cylinder Onto Its Core

Contractible Products and Coordinate Homotopies

Contractible Spaces and Contraction Maps

Composing Homotopies With Continuous Maps