Does every non-compact Tychonoff space admit an unbounded continuous function?
45249
Pseudocompactness does not imply compactness
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
64619
Continuity of a function of product spaces
57014
Existence of a power series converging non-uniformly to a continuous function
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
22641
Nonlinear function continuous but not bounded
59519
What about the continuity of these functions in the uniform topology?
13506
Can an unbounded function have a finite integral?
2118
Are continuous functions with compact support bounded?
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
15487
Continuous function from a connected set?
99675
A closed ball in $l^{\infty}$ is not compact
12349
a construction of a continuous function from a normal space to [0,1]
76607
Show that exists a continuous function in $E$ that is not bounded
86782
A $T_4$ space satisfying that 'every continuous map from it to a Hausdorff space is a closed map' is compact.