Remark

If $X$ is a normal space and if $A$ is a closed subset of $X$, there exists also a continuous extension to $X$ of every continuous mapping $f$ of $A$ into a cube $K^1$ (§ 1, no. 5); for we have then $f = (f_i)_{i \in I}, f_i$ being a continuous mapping of $A$ into the compact interval $K$ of $\mathbf{R}$; since there exists a continuous mapping $g_i : X \to K$ which extends $f_i$, the mapping $g = (g_i)$ is a continuous extension of $f$ to $X$.