Definition of continuity of open balls or delta
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
42084
Set of points of continuity are $G_{\delta}$
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
109570
How to show that the set of points of continuity is a $G_{\delta}$
9614
How does the existence of a limit imply that a function is uniformly continuous
157384
Points of continuity is a Borel set?
59519
What about the continuity of these functions in the uniform topology?
135661
Weakly continuous operators are continuous
110146
I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
60521
Continuity of a convex function
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
70645
Borel set preserved by continuous map
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
90152
Continuous with compact support implies uniform continuity
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
135454
An open interval is an open set?