smooth functions are dense in the space of bounded continuous functions - why?
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions
97064
Dense set in an infinite cofinite space
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
34836
Composition of Absolutely Continuous Functions
158011
$C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
101906
Why is this sequence of equicontinuous functions uniformly bounded?
66691
Real function continuous on closed interval implies it is bounded - over-simple proof??
40297
Proof of uniform limit of Continuous Functions
61122
A continuous mapping is determined by its values on a dense set
64619
Continuity of a function of product spaces
9614
How does the existence of a limit imply that a function is uniformly continuous
71001
Do continuous linear functions between Banach spaces extend?
146846
Why is this function continuous, unlike the Dirichlet function?
118400
Is there a monotonic function discontinuous over some dense set?
141842
Is the convolution of two continuous functions continuous?
7861
Non-analytic smooth function