show that if A is not compact, exists a function continuous and bounded without maximum or minimum
76607
Show that exists a continuous function in $E$ that is not bounded
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
91398
Continuous function on R which tends to infinity on open interval must have a minimum
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
151410
Inequality of continuous functions
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
65346
Characterisation of uniformly continuous function
60521
Continuity of a convex function
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
17234
Show that a continuous function has a fixed point
127739
Is a continuous function on a bounded set bounded itself?
34344
Is a function that maps every compact set to a compact set continuous?
154572
Continuity of a function at an isolated point
28637
Proving continuous image of compact sets are compact