The fine spectrum of the Cesàro operator in the sequence space

${c}_{0}$ is examined. Although the spectrum of the Cesàro operator in the sequence space

${c}_{0}$ was already determined by

*J. B. Reade* [Bull. Lond. Math. Soc. 17, 263–267 (1985;

Zbl 0548.47017)] and others, the results of the present paper give a refinement of the previous works. Further, a Mercerian theorem is also stated and proved. Finally, the fine spectrum of the Cesàro operator in the sequence space

$c$ is given, without proof.