Corollary 3

Let X be a normal topological space, let A be a closed subspace of X and let U be a neighbourhood of A in X. Let Z be a topological space homotopic to a point and let $g: U\rightarrow$ Z be a continuous mapping. There exists a continuous mapping $\widetilde{g}: X\rightarrow Z$ which coincides with $g$ on A.

Since Z is homotopic to a point, the mapping $g$ is homotopic to a constant mapping $f$. The mapping $f$ extends continuously to X ; the assertion therefore follows from Cor. 2.