Paul starts his letter with a universal salutation:

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           To the church of God in Corinth, to those sanctified in Christ Jesus and called to be holy, together with all those everywhere who call on the name of our Lord Jesus Christ (1 Cor 1:2).
    
Despite their problems, the Corinthians are "sanctified" by the fact that they called on the name of Jesus to be saved.   The result is that they are "set apart" -- holy -- though not yet completely.  One of the obstacles they faced is the existence of factions in the church -- not along racial lines, but following different leaders, including Paul himself.