1. Does Monotone Locally Bounded Function Definitely Have Extreme?

2. Theorem 2 The product of bounded function and an infinitesimal is an infinitesimal.

3. Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

4. Continuous Bounded function on the Bounded open interval ]a,b[ that is not uniformly continuous on ]a,b 2 Is $\frac{1}{\sin x}-\frac{1}{x}$ uniformly continuous on $(0,1)$?