  Given a compact, metric space X, we show that the commutative C*-algebra C(X)
is semiprojective if and only if X is an absolute neighborhood retract of
dimension at most one. This confirms a conjecture of Blackadar. Generalizing to
the non-unital setting, we derive a characterization of semiprojectivity for
separable, commutative C*-algebras. As further application of our findings we
verify two conjectures of Loring and Blackadar in the commutative case, and we
give a partial answer to the question, when a commutative C*-algebra is weakly
(semi-)projective.
