We say that a topological space $(X,\tau)$ is *flexible*, if for every closed discrete subset $D\subseteq X$ and every map $f: D\to X$ there is a continous map $f^X:X\to X$ such that $f^X|_D = f$.

$\mathbb{R}$ with the Euclidean topology is flexible.

Is every homogeneous $T_2$-space flexible?

**Note.** I called spaces with the above property "flexible" because they are in some sense the opposite of (strongly) rigid spaces; flexible spaces admit a lot of continuous self-maps, and strongly rigid spaces only very few.