A set is compact if and only if every continuous function is bounded on the set?
51853
$K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
95993
Isn't every subset of a compact space compact?
47188
Uniformly Continuous Function sending Bounded Set to Unbounded One
9268
Proving that the Union of Two Compact Sets is Compact
83461
Continuous iff composition with every linear functional is continuous
36166
Uniform continuity on (0,1) implies boundedness
90152
Continuous with compact support implies uniform continuity
135157
Totally bounded, complete $\implies$ compact
136011
Must $f$ be continuous?
2118
Are continuous functions with compact support bounded?
14219
Is the intersection of a closed set and a compact set always compact?
136583
Infimum is a continuous function, compact set
40915
Proof if $f$ continuous in $x_0$ then there is a neighbourhood of $x_0$ so f bounded.
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
143618
If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?