Points at which function is continuous is countable intersection of open sets
109570
How to show that the set of points of continuity is a $G_{\delta}$
112409
If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing
126842
Fixed point in a continuous function
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
77621
Continuity of function mapping connected set to connected set
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
55749
Compactly supported continuous function is uniformly continuous
154572
Continuity of a function at an isolated point
71487
Real Analysis: Continuity of a Composition Function
34836
Composition of Absolutely Continuous Functions
125610
Space of bounded continuous functions is complete
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
16654
Unions and Intersections of Open Sets are Open
79490
Proving the set of points at which a function diverges to $\infty$ is countable
29154
$f$ is continuous and open implies $f$ injective
42794
Prove that functions map countable sets to countable sets
152784
$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.