A set $A\in \Bbb{R}^n$ is compact $\iff$ every continuous function on $A$ is bounded.
51853
$K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
30210
A compact operator is completely continuous.
36149
A uniformly continuous function maps bounded set to bounded sets
44647
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
9268
Proving that the Union of Two Compact Sets is Compact
106534
"Closed subsets of compact space are compact" with an alternative definition of covering
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
86309
Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
157821
Let $S$ be a finite set. Show that any function $f: S \rightarrow \mathbb{R}^n$ is continuous on S. What if $S$ is countably infinite?
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
18040
Show that a compact metric space is bounded
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
118765
A topological space is locally compact then here is an open base at each point has all of its set with compact closure
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space