Other than its supreme composition of analytical essence,this small(but really important)example shows more vividly why theres Tao's book at the supremum:-Given a sequence of functions from one metric space(x,dx) to other(y,dy),if they uniformly converge to some function f(x)|f(x):x->y ,then unlike the sequence of 'points',the functions wont converge to eider in space (x) or space (y) but totally in a new space of functions from x to y!Thats the quality rigor which has every commandment over the subject...
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