492 
DISCONTINUOUS FUNCTIONS 
2. Iff is semicontinuous in the complete set 91, it is at most point- 
wise discontinuous in 91. 
* 01 ®O0 =70) -/0*0 
. = [70) “/(*)] + C/O) -/0*0] (1 
= <¿>0*0 + ^0*0- 
To fix the ideas let / be supracontinuous. Then </> = 0 in 91. 
Hence 1) gives 
Min a>(x) = Min y\r(x) = 0, by 1. 
Thus by 496, 3, f is at most pointwise discontinuous in 91.