Let F: [0,1]X[0,1] --> R

where F is such st both Fy(x) and Fx(y) are continuous. [That is, Fy(x) is the function holding y constant]

Furthermore, assume that the set of functions, E, is equicontinuous. Where E

E = {maps that take x-->f(x,y) : y is in [0,1]}

Prove that f is continuous.

I guess my biggest problem is that I'm not entirely clear what the set E represents. Is E the set of all {Fy(x) for all y in [0,1]}?