Mapping Cylinder

- Mathematics & Logic -
Pure Mathematics Dictionary
Given a continuous map f: X→Y, the mapping cylinder Mf is the space obtained by taking X×[0,1] disjoint union Y and identifying each (x,1)∈X×{1} with f(x)∈Y; equivalently it is X×[0,1] ⊔_f Y. It provides a model for a homotopy between f and a cofibration inclusion of X into Mf.