Prove $\exists$ a sequence of polynomials which converges to $f$ on any compact subset of $\mathbb{R}$.
136594
Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
148349
Uniform convergence with two sequences of functions
55826
Convergence of sequence of real numbers and (sub)subsequence
87086
Equivalence of convergence in products of sequences.
52711
Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
140972
Uniform convergence of harmonic functions to $0$ on compact subsets
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
104033
Confused with proof that all Cauchy sequences of real numbers converge.
53001
If $|f'(c)| \leq M$ and $ M < 1$, the sequence defined by $a_{n+1} = f(a_n)$ converges
112773
With $y_n$ a sequence of real numbers, prove that if $y_n=x_{n-1}+2x_{n}$ converges then $x_n$ also converges
14836
A polynomial sequence
39230
Even function has even sequences of polynomials converging uniformly?
75614
Proving that $n|m\implies f_n|f_m$
143942
Verify proof that sequence converges
32630
Proving that a set in which any sequence having exactly one accumulation point converges is compact
44717
Does there exist a bijective $f:\mathbb{N} \to \mathbb{N}$ such that $\sum f(n)/n^2$ converges?
55337
Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.