Is a set of continuous and bounded functions defined on [0,1] compact? Is it bounded?
98756
Unit ball in $C[0,1]$ not sequentially compact
18040
Show that a compact metric space is bounded
15487
Continuous function from a connected set?
136583
Infimum is a continuous function, compact set
19111
If every real-valued continuous function is bounded on $X$ (metric space), then $X$ is compact.
47810
$C(X)$ is separable when $X$ is compact?
41408
Which of the following sets are compact:
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
124959
Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
132413
$f \in C^1$ defined on a compact set $K$ is Lipschitz?
12003
Cardinality of set of real continuous functions
12349
a construction of a continuous function from a normal space to [0,1]
66691
Real function continuous on closed interval implies it is bounded - over-simple proof??
132946
Continuous and bounded imply uniform continuity?
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$