Let f : [a,b] > R. Let x0 6 [a,b]. Then f is said to be upper semicontinuous (use) at x0 if limsup f (x) S f (x0). x>x0 x6 [a,b] A function is upper semicontinuous on [a,b] if it is use for all x 6 [a,b]. Show that a function is use on [a, b] if and only if {x E [a, b] : f (x) 2 a} is closed for all a in R