counterexample sequence of continuous function converges to continuous function pointwise implies uniform convergence
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
148349
Uniform convergence with two sequences of functions
80622
Lebesgue integral uniform convergence
90152
Continuous with compact support implies uniform continuity
41057
Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?
88610
The set of convergence of a sequence of measurable functions is measurable
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
138317
weak convergence in $l^p$ implies bounded and pointwise convergence
66198
Sufficient condition for convergence of a real sequence
36149
A uniformly continuous function maps bounded set to bounded sets
47693
Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.
13257
How to prove this problem about uniform continuity
144957
Uniform convergence of a function
71140
Pointwise limit of the sequence of continuously differentiable functions defined inductively.
55749
Compactly supported continuous function is uniformly continuous
140445
Sequence of continuous functions whose pointwise limit is discontinuous