# Which compacta are noncommutative ARs - Mathematics > Operator Algebras

Abstract: We give a short answer to the question in the title: {\em dendrits}.Precisely we show that the $C^{\ast}$-algebra $CX$ of all complex-valuedcontinuous 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.

Author: A.Chigogidze, A.N.Dranishnikov

Source: https://arxiv.org/