btw all the large As and Bs should actually be small and the a ---> det(a) should actually be large; A----> det(A). Any help is valued thnx.
the point is, det is a function from . you should already know that s(x,y) = x+y is continuous from , and that p(x,y) = xy is continuous from .
so det(a,b,c,d) = s(p(a,d),-p(b,c)), which is a composition of continuous maps, yes?