Suppose $\partial_j \partial_i f$ is continuous at $a$ and $\partial_j f$ exists. Then $\partial_i \partial_j f (a) = \partial_j \partial_i f (a)$
70438
Generalize Clairaut-Schwarz theorem to arbitrary order of mixed partial derivatives
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
144013
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
32359
Inner product of two continuous maps is continuous
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
64619
Continuity of a function of product spaces
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
31747
Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
17223
Continuity of an inverse function.
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
43874
Differentiability implies continuity - A question about the proof
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
28730
product of two uniformly continuous functions is uniformly continuous