2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220421We give a short answer to the question in the title: {\em dendrits}. Precisely we show that the $C^{\ast}$-algebra $C(X)$ of all complex-valued continuous functions on a compactum $X$ is projective in the category ${\mathcal C}^{1}$ of all (not necessarily commutative) unital $C^{\ast}$-algebras if and only if $X$ is an absolute retract of dimension $\dim X \leq 1$ or, equivalently, that $X$ is a dendrit.8 pagesOperator AlgebrasGeometric Topology46M10text