Sequential Continuity does not imply Continuity
34298
sequentially continuous on a non first-countable
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
146707
Formally show that the set of continuous functions is not measurable
79417
A "non-trivial" example of a Cauchy sequence that does not converge?
34527
How to show a sequence of independent random variables do not almost surely converge by definition?
81929
d-metrizable spaces are sequential
145017
Example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points
110258
Continuous but not uniformly continuous example
100436
Examples of nowhere continuous functions
71487
Real Analysis: Continuity of a Composition Function
138815
For which conditions on countable sets does continuity implies uniform continuity
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
123357
Real Analysis - A sequence that has no convergent subsequence
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
153495
Continuous function does not map closed set to closed set
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
100786
Does a continuous function take Cauchy sequences to Cauchy sequences?