On injections and surjections of continuous function spaces

It is shown that a linear isometry ofC(S) intoC(T) is generated by a linear extension fromS to a quotient space ofT. A dual theorem is proved for a quotient map ofC(S) ontoC(T). An application of the first theorem and a modification of a theorem by Banach and Mazur provide a negative answer to a problem posed by Pelczynski.