Let F = ( f1 (Ā,X¯ ), . . ., fl (Ā,X¯ )) be a finite set of polynomials in Q[Ā,X¯ ] with variables Ā = A1, . . .,Am and X¯ = X1, . . .,Xn . We study the continuity of the map θ from an element ā of Cm to a subset of Cn defined by θ (ā) = “the zeros of the polynomial ideal hf1 (ā,X¯ ), . . ., fl (ā,X¯ )i”. Let G = ((G1, S1), . . ., (Gk , Sk )) be a comprehensive Gröbner system of hF i regarding Ā as parameters. By a basic property of a comprehensive Gröbner system, when the ideal hf1 (ā,X¯ ), . . ., fl (ā,X¯ )i is zero dimensional for some ā ∈ Si , it is also zero dimensional for any ā ∈ Si and the cardinality of θ (ā) is identical on Si counting their multiplicities. In this paper, we prove that θ is also continuous on Si . Our result ensures the correctness of an algorithm for real quantifier elimination one of the authors has recently developed.