Pick the correct statement(s) from below. (A) If $f$ is continuous and bounded on $( 0,1 )$, then $f$ is uniformly continuous on $( 0,1 )$. (B) If $f$ is uniformly continuous on $( 0,1 )$, then $f$ is bounded on $( 0,1 )$. (C) If $f$ is continuous on $( 0,1 )$ and $\lim _ { x \rightarrow 0 ^ { + } } f ( x )$ and $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$ exists, then $f$ is uniformly continuous on $( 0,1 )$. (D) Product of a continuous and a uniformly continuous function on $[ 0,1 ]$ is uniformly continuous.
Pick the correct statement(s) from below.\\
(A) If $f$ is continuous and bounded on $( 0,1 )$, then $f$ is uniformly continuous on $( 0,1 )$.\\
(B) If $f$ is uniformly continuous on $( 0,1 )$, then $f$ is bounded on $( 0,1 )$.\\
(C) If $f$ is continuous on $( 0,1 )$ and $\lim _ { x \rightarrow 0 ^ { + } } f ( x )$ and $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$ exists, then $f$ is uniformly continuous on $( 0,1 )$.\\
(D) Product of a continuous and a uniformly continuous function on $[ 0,1 ]$ is uniformly continuous.