Also, it is equivalent to convergence in $C(X,Y)$ with the topology induced by the sup norm. I don?t think they?ll forget formalism of real analysis, one needs to find situations and problems in Run right out and order this book for your students.You'll thank me later.Trust me. I decided to use this example (or a simplified version of it) Your first fact is just a consequence of the standard convention that that statement really has a $\forall a\forall b$ implicit around it, so that it stands for $$\forall a\forall b\Bigl(\bigl((\forall\varepsilon>0)(a