The problem of simultaneous Chebyshev approximation of a set F F of uniformly bounded, real-valued functions on a compact interval I I . by a set P P of continuous functions is equivalent to the problem of simultaneous approximation of two real-valued functions F + ( x ) , F − ( x ) {F^ + }(x),{F^ - }(x) , with F − ( x ) ≦ F + ( x ) {F^ - }(x) \leqq {F^ + }(x) , for all x x in I I , where F − {F^ - } is lower semicontinuous and F − {F^ - } is upper semicontinuous.