Is the function $f(x) = \frac{1}{x}$ uniformly continuous on the interval $(0.2 ,1)$?

Question

Is the function $f(x) = \frac{1}{x}$ uniformly continuous on the interval $(0.2, 1)$?

edit1: I know from my textbook and other posts that the function $f(x) = \frac{1}{x}$ is not uniformly continuous on intervals such as $(0,1]$.

Answer 1

By the Heine-Cantor theorem, it is uniformly continuous on each bounded and closed interval not containing $0$.

Moreover, obviously, if it is continuous on $[0.2, 1]$, it is uniformly continuous on each interval contained in it.