# Definition Homotopy type is an [[Equivalence Class]] somewhat coarser than the [[Homeomorphism|homeomorphism class]]. The difference is that the homotopy type [[map]] need not have an inverse, but they remain [[Continuous Map|continuous]]. See the definition of [[homeomorphism]]. # Examples * $\mathbb{R}^3 - \{.\pmb{0}\}$ and $S^2$ ([[2-sphere|S^2]]) are of the same homotopy type. * A [[circle]] $S^1$ and a [[cylinder]] $S^1 \times \mathbb{R}$ are of the same homotopy type.