Solution to Understanding Analysis Exercise 4.4
Exercise 4.4.1 See Understanding Analysis Instructors’ Solution Manual Exercise 4.4.1. Exercise 4.4.2 (a) No, let $x_n=\dfrac{1}{n}$ and $y_n=\dfrac{1}{2n}$, then\[|x_n-y_n|=\frac{1}{2n}\to 0,\quad |f(x_n)-f(y_n)|=n\geqslant 1.\]Hence by Theorem 4.4.5, $f(x)$ is not uniformly continuous…