Prove or disprove that if f is continuous on a bounded set S, then f is bounded function on S
127739
Is a continuous function on a bounded set bounded itself?
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
51853
$K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
104044
Prove continuous functions $f$ and $g$ are equal
122086
continuous function: preimage of closure of a set is closure of preimage
53738
Monotone functions and continuity
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
87239
Prove functions defined by sup and inf are continuous
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
121957
Is $p\mapsto \|f\|_p$ continuous?
53627
Proving continuity of $f$
113122
Prove that a continuous real function with finite limits is bounded
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous